https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Moises&feedformat=atomUWMath Wiki  User contributions [en]20200814T15:30:07ZUser contributionsMediaWiki 1.30.1https://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=17313Graduate Algebraic Geometry Seminar20190414T15:36:00Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
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* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
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* What and why is a dessin d'enfants?<br />
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* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2019 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 6<br />
 bgcolor="#C6D46E" Vlad Sotirov<br />
 bgcolor="#BCE2FE"[[#February 6 Heisenberg Groups and the Fourier Transform]]<br />
<br />
 bgcolor="#E0E0E0" February 13<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[#February 13 DG potpourri]]<br />
<br />
 bgcolor="#E0E0E0" February 20<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[#February 20 Completions of Noncatenary Local Domains and UFDs]]<br />
<br />
 bgcolor="#E0E0E0" February 27<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[#February 27 Baker’s Theorem]]<br />
<br />
 bgcolor="#E0E0E0" March 6<br />
 bgcolor="#C6D46E" Connor Simpson<br />
 bgcolor="#BCE2FE"[[#March 6 Mason's Conjectures and Chow Rings of Matroids]]<br />
<br />
 bgcolor="#E0E0E0" March 13<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[#March 13 Dial M_1,1 for moduli]]<br />
<br />
 bgcolor="#E0E0E0" March 27<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[#March 27 Quadratic Forms]]<br />
<br />
 bgcolor="#E0E0E0" April 3<br />
 bgcolor="#C6D46E" Colin Crowley<br />
 bgcolor="#BCE2FE"[[#April 3 RiemannRoch and AbelJacobi theory on a finite graph]]<br />
<br />
 bgcolor="#E0E0E0" April 10<br />
 bgcolor="#C6D46E" Alex Hof<br />
 bgcolor="#BCE2FE"[[#April 10 Kindergarten GAGA]]<br />
<br />
 bgcolor="#E0E0E0" April 17<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[#April 17 Inseparable maps and quotients of varieties]]<br />
<br />
 bgcolor="#E0E0E0" April 24<br />
 bgcolor="#C6D46E" Wendy Cheng<br />
 bgcolor="#BCE2FE"[[#April 24 Title]]<br />
<br />
 bgcolor="#E0E0E0" May 1<br />
 bgcolor="#C6D46E" Shengyuan Huang<br />
 bgcolor="#BCE2FE"[[#May 1 Orbifold Singular Cohomology]]<br />
}<br />
</center><br />
<br />
== February 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Heisenberg Groups and the Fourier Transform<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE"  Title: DG potpourri<br />
<br />
 bgcolor="#BCD2EE"  Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
<br /><br />
[[File:Dgmeme.pngcenter]]<br />
} <br />
</center><br />
<br />
== February 20 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Completions of Noncatenary Local Domains and UFDs<br />
<br />
 bgcolor="#BCD2EE"  Abstract: A ring is called catenary if for any pair of prime ideals P contained in Q, all saturated chains of prime ideals between P and Q have the same length.<br />
In this talk, I will introduce the necessary background about noncatenary rings and completions of local (Noetherian) domains, as well as the relevant history. Then, I will give the characterization of completions of noncatenary local domains and noncatenary local UFDs, which I will use to describe examples of very strange rings.<br />
} <br />
</center><br />
<br />
== February 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Sun Woo Park'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Baker's Theorem<br />
<br />
 bgcolor="#BCD2EE"  Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
<br /><br />
[[File:Sun_woo_baker.png500pxcenter]]<br />
} <br />
</center><br />
<br />
== March 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Connor Simpson'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Mason's Conjectures and Chow Rings of Matroids<br />
<br />
 bgcolor="#BCD2EE"  Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Dial M_1,1 for moduli<br />
<br />
 bgcolor="#BCD2EE"  Abstract: We will speculate wildly about what kind of object the moduli space of elliptic curves should be. I don't know what a stack is, and I promise not to try to define one.<br />
<br/><br />
[[File:DialMForElliptic.png400pxcenter]]<br />
} <br />
</center><br />
<br />
== March 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Quadratic Forms<br />
<br />
 bgcolor="#BCD2EE"  Abstract: Starting from the classical story of binary quadratic forms, we'll move on to more modern aspects of the theory of quadratic forms and try to make sense of some mass formulas.<br />
} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Colin Crowley'''<br />
<br />
 bgcolor="#BCD2EE"  Title: RiemannRoch and AbelJacobi theory on a finite graph<br />
<br />
 bgcolor="#BCD2EE"  Abstract: A finite graph is like a Riemann surface, or a smooth projective curve. Following the paper by Baker and Norine, we will investigate linear equivalence of divisors on graphs, the Jacobian of a graph, and a combinatorial interpretation of these as a chip firing game.<br />
} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Alex Hof'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Kindergarten GAGA<br />
<br />
 bgcolor="#BCD2EE"  Abstract: Join me in regressing to an infantile state as we discuss Serre's 1956 paper ''Algebraic geometry and analytic geometry'', widely considered to be the most influential work ever authored by a mathematician under the age of five. We will define the notion of an analytic space, construct the analytic space associated to any algebraic variety over <math>\mathbb{C}</math>, and examine the relationships between the two, including the equivalence between coherent algebraic sheaves and coherent analytic sheaves in the projective case.<br />
<br />
[[File:Badromancehof.png500pxcenter]]<br />
} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Inseparable maps and quotients of varieties<br />
<br />
 bgcolor="#BCD2EE"  Abstract: TBA<br />
<br />
[[File:Prime_Characteristic.jpg500pxcenter]]<br />
} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Name'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Shengyuan Huang'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Orbifold Singular Cohomology<br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=File:Prime_Characteristic.jpg&diff=17312File:Prime Characteristic.jpg20190414T15:34:18Z<p>Moises: </p>
<hr />
<div></div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=K3_Seminar_Spring_2019&diff=17229K3 Seminar Spring 201920190328T15:44:23Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Thursday 57 pm<br />
<br />
'''Where:''' Van Vleck B135<br />
<br />
'''<br />
<br />
<br />
<br />
== Schedule ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title'''<br />
<br />
 bgcolor="#E0E0E0" March 7<br />
 bgcolor="#C6D46E" Mao Li<br />
 bgcolor="#BCE2FE"[[#March 7 Basics of K3 Surfaces and the GrothendieckRiemannRoch theorem]]<br />
<br />
 bgcolor="#E0E0E0" March 14<br />
 bgcolor="#C6D46E" Shengyuan Huang<br />
 bgcolor="#BCE2FE"[[#March 14 Elliptic K3 Surfaces]]<br />
<br />
 bgcolor="#E0E0E0" March 28<br />
 bgcolor="#C6D46E" Zheng Lu<br />
 bgcolor="#BCE2FE"[[#March 28 Moduli of Stable Sheaves on a K3 Surface]]<br />
<br />
 bgcolor="#E0E0E0" April 4<br />
 bgcolor="#C6D46E" Canberk Irimagzi<br />
 bgcolor="#BCE2FE"[[#April 4 FourierMukai Transforms]]<br />
<br />
 bgcolor="#E0E0E0" April 11<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[#April 11 Cohomology of Complex K3 Surfaces and the Global Torelli Theorem]]<br />
<br />
 bgcolor="#E0E0E0" April 25<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[#April 25 Derived Categories of K3 Surfaces]]<br />
}<br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Mao Li'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Basics of K3 Surfaces and the GrothendieckRiemannRoch theorem<br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
}<br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Shengyuan Huang'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Elliptic K3 Surfaces<br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== March 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Zheng Lu'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Moduli of Stable Sheaves on a K3 Surface<br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Canberk Irimagzi'''<br />
<br />
 bgcolor="#BCD2EE"  Title: FourierMukai Transforms<br />
<br />
 bgcolor="#BCD2EE"  Abstract: I will describe Chow theoretic correspondences as a motivation to derived correspondences. We will then define integral functors on derived categories. The dual abelian variety will be given as a moduli space in terms of its functor of points, leading us to a definition of the universal Poincaré bundle on $A \times \hat{A}$. We will look at the integral transform from $D(A)$ to $D(\hat{A})$ induced by the Poincaré bundle. Cohomology of the Poincaré bundle will be stated and used for the computation of the $K$theoretic FourierMukai transform on elliptic curves. With the help of the base change theorem, we will describe the FourierMukai duals of homogeneous line bundles on $A$. For an elliptic curve $E$, we will establish the equivalence between<br />
<br />
1. the abelian category of semistable bundles of slope 0 on $E$, and <br />
<br />
2. the abelian category of coherent torsion sheaves on $E$. <br />
<br />
Simple and indecomposable objects of these categories will be described (with the help of the structure theorem of PIDs) and we will relate this picture to Atiyah’s classification of the indecomposable vector bundles of degree 0.<br />
<br />
} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Cohomology of Complex K3 Surfaces and the Global Torelli Theorem<br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto<br />
'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Derived Categories of K3 Surfaces<br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== Contact Info ==<br />
<br />
To get on our mailing list, please contact<br />
<br />
[mailto:irimagzi@wisc.edu Canberk Irimagzi]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=17211Madison Math Circle20190325T05:16:03Z<p>Moises: </p>
<hr />
<div>[[Image:logo.pngright440px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg500px]] [[Image: MathCircle_4.jpg500px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/schoolspotlightmadisonmathcirclegivesyoungstudentsataste/article_77f5c0420b3d11e1ba5f001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UWMadison campus, right next to the Memorial Union).<br />
<br />
<br />
==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; marginleft:auto; marginright:auto;"><br />
[[File: Helencwhitemap.png400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UWMadison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to joinmathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UWMadison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@lists.wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
File:Betsy.jpg[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]<br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
File:juliettebruce.jpg[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]<br />
File:Ee.jpg[http://www.math.wisc.edu/~evaelduque/ Eva Elduque]<br />
File:mrjulian.jpg[http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
File:soumyasankar.jpg[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]<br />
</gallery><br />
</center><br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
<br />
So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for recordkeeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can just pay in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
*Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students<br />
*Discussing the Math Circle with students, parents, teachers, administrators, and others<br />
*Making an announcement about Math Circle at PTO meetings<br />
*Donating to Math Circle<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Meetings for Spring 2019=<br />
<br />
<center><br />
<br />
Talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
{ style="color:black; fontsize:120%" border="1" cellpadding="14" cellspacing="0"<br />
<br />
! colspan="3" style="background: #e8b2b2;" align="center"  Spring 2019<br />
<br />
! Date !! Speaker !! Topic<br />
<br />
 January 28, 2019  CANCELLED  Madison's schools are closed<br />
<br />
 February 4, 2019  Stephen Davis  Newton's law of gravity<br />
<br />
 February 11, 2019  Yandi Wu  Surfaces and "Cut and Paste Topology"<br />
<br />
 February 18, 2019  Michel Alexis  Kakeya Needle Sets<br />
<br />
 February 25, 2019  Colin Crowley  Regular Languages<br />
<br />
 March 4, 2019  Jenny Yeon  Where do numbers like "1/3" and "1/4" in volume formulas come from?<br />
<br />
 March 11, 2019  Chaojie Yuan  A region of finite area with infinite perimeter<br />
<br />
 March 18, 2019  No Meeting  Spring Break<br />
<br />
 March 25, 2019  Eva Elduque  Will it fold flat?<br />
<br />
 April 1, 2019  Alex Mine  TBD<br />
<br />
 April 8, 2019  Caitlyn Booms  TBD<br />
<br />
 April 15, 2019  Polly Yu  Chaos and unavoidable patterns<br />
}<br />
<br />
</center><br />
<br />
=Meetings for Fall 2018=<br />
<br />
<center><br />
<br />
Unless specified talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
{ style="color:black; fontsize:120%" border="1" cellpadding="14" cellspacing="0"<br />
<br />
! colspan="3" style="background: #e8b2b2;" align="center"  Fall 2018<br />
<br />
! Date !! Speaker !! Topic<br />
<br />
 September 17, 2018  Sun Woo Park  Why are Donuts and Cream Puffs "different"?<br />
<br />
 September 24, 2018  Ben Bruce  Three Cottages Problem<br />
<br />
 October 1, 2018  Kit Newton  How to calculate Pi if all you can do is throw things<br />
<br />
 October 8, 2018  Connor Simpson  TBD<br />
<br />
 October 15, 2018  JeanLuc Thiffeault  TBD<br />
<br />
 October 22, 2018  Patrick Nicodemus  Formal Systems in Computer Science and Logic<br />
<br />
 October 29, 2018  Moisés Herradón Cueto  Order and chaos in population sizes ([http://www.math.wisc.edu/~moises/Math_Circle_Talk.html try it yourself!])<br />
<br />
 November 5, 2018  Christian Geske  Josephus Problem<br />
<br />
 November 12, 2018  Rachel Davis  TBD<br />
<br />
 November 19, 2018  Uri Andrews  King Chicken<br />
<br />
}<br />
<br />
</center><br />
<br />
=OffSite Meetings=<br />
<br />
We will hold some Math Circle meetings at local high schools on early release days. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<br />
<center><br />
<br />
{ style="color:black; fontsize:120%" border="1" cellpadding="14" cellspacing="0"<br />
<br />
! colspan="5" style="background: #e8b2b2;" align="center"  Fall 2017<br />
<br />
<br />
! Date !! Time !! Location !! Speaker !! Topic <br />
<br />
 October 29th  2:45pm East High School  Madison, WI  TBD  TBD <br />
<br />
 December 3rd  2:45pm East High School  Madison, WI  TBD  TBD<br />
<br />
}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 20132014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_20162017 2016  2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_20162017 2016  2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_20152016 2015  2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_20152016 2015  2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_20152016 2015  2015 Abstracts]<br />
<br />
[[Archived Math Circle Material]]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.mathcircles.org/content/lessonplans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circlebox "Circle in a Box"]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=17141Graduate Algebraic Geometry Seminar20190311T22:33:03Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2019 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 6<br />
 bgcolor="#C6D46E" Vlad Sotirov<br />
 bgcolor="#BCE2FE"[[#February 6 Heisenberg Groups and the Fourier Transform]]<br />
<br />
 bgcolor="#E0E0E0" February 13<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[#February 13 DG potpourri]]<br />
<br />
 bgcolor="#E0E0E0" February 20<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[#February 20 Completions of Noncatenary Local Domains and UFDs]]<br />
<br />
 bgcolor="#E0E0E0" February 27<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[#February 27 Baker’s Theorem]]<br />
<br />
 bgcolor="#E0E0E0" March 6<br />
 bgcolor="#C6D46E" Connor Simpson<br />
 bgcolor="#BCE2FE"[[#March 6 Mason's Conjectures and Chow Rings of Matroids]]<br />
<br />
 bgcolor="#E0E0E0" March 13<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[#March 13 Dial M_1,1 for moduli]]<br />
<br />
 bgcolor="#E0E0E0" March 27<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[#March 27 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 3<br />
 bgcolor="#C6D46E" Colin Crowley<br />
 bgcolor="#BCE2FE"[[#April 3 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 10<br />
 bgcolor="#C6D46E" Alex Hof<br />
 bgcolor="#BCE2FE"[[#April 10 Kindergarten GAGA]]<br />
<br />
 bgcolor="#E0E0E0" April 17<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[#April 17 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 24<br />
 bgcolor="#C6D46E" Wendy Cheng<br />
 bgcolor="#BCE2FE"[[#April 24 Title]]<br />
<br />
 bgcolor="#E0E0E0" May 1<br />
 bgcolor="#C6D46E" Shengyuan Huang<br />
 bgcolor="#BCE2FE"[[#May 1 Orbifold Singular Cohomology]]<br />
}<br />
</center><br />
<br />
== February 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Heisenberg Groups and the Fourier Transform<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE"  Title: DG potpourri<br />
<br />
 bgcolor="#BCD2EE"  Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
<br /><br />
[[File:Dgmeme.pngcenter]]<br />
} <br />
</center><br />
<br />
== February 20 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Completions of Noncatenary Local Domains and UFDs<br />
<br />
 bgcolor="#BCD2EE"  Abstract: A ring is called catenary if for any pair of prime ideals P contained in Q, all saturated chains of prime ideals between P and Q have the same length.<br />
In this talk, I will introduce the necessary background about noncatenary rings and completions of local (Noetherian) domains, as well as the relevant history. Then, I will give the characterization of completions of noncatenary local domains and noncatenary local UFDs, which I will use to describe examples of very strange rings.<br />
} <br />
</center><br />
<br />
== February 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Sun Woo Park'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Baker's Theorem<br />
<br />
 bgcolor="#BCD2EE"  Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
<br /><br />
[[File:Sun_woo_baker.png500pxcenter]]<br />
} <br />
</center><br />
<br />
== March 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Connor Simpson'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Mason's Conjectures and Chow Rings of Matroids<br />
<br />
 bgcolor="#BCD2EE"  Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Dial M_1,1 for moduli<br />
<br />
 bgcolor="#BCD2EE"  Abstract: We will speculate wildly about what kind of object the moduli space of elliptic curves should be. I don't know what a stack is, and I promise not to try to define one.<br />
<br/><br />
[[File:DialMForElliptic.png400pxcenter]]<br />
} <br />
</center><br />
<br />
== March 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract:<br />
} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Colin Crowley'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Alex Hof'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
<br />
[[File:Badromancehof.png500pxcenter]]<br />
} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Name'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Shengyuan Huang'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Orbifold Singular Cohomology<br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=File:DialMForElliptic.png&diff=17140File:DialMForElliptic.png20190311T22:29:53Z<p>Moises: </p>
<hr />
<div></div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=17077Graduate Algebraic Geometry Seminar20190301T21:44:09Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2019 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 6<br />
 bgcolor="#C6D46E" Vlad Sotirov<br />
 bgcolor="#BCE2FE"[[#February 6 Heisenberg Groups and the Fourier Transform]]<br />
<br />
 bgcolor="#E0E0E0" February 13<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[#February 13 DG potpourri]]<br />
<br />
 bgcolor="#E0E0E0" February 20<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[#February 20 Completions of Noncatenary Local Domains and UFDs]]<br />
<br />
 bgcolor="#E0E0E0" February 27<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[#February 27 Baker’s Theorem]]<br />
<br />
 bgcolor="#E0E0E0" March 6<br />
 bgcolor="#C6D46E" Connor Simpson<br />
 bgcolor="#BCE2FE"[[#March 6 Mason's Conjectures and Chow Rings of Matroids]]<br />
<br />
 bgcolor="#E0E0E0" March 13<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[#March 13 Dial M_1,1 for moduli]]<br />
<br />
 bgcolor="#E0E0E0" March 27<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[#March 27 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 3<br />
 bgcolor="#C6D46E" Colin Crowley<br />
 bgcolor="#BCE2FE"[[#April 3 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 10<br />
 bgcolor="#C6D46E" Alex Hof<br />
 bgcolor="#BCE2FE"[[#April 10 Kindergarten GAGA]]<br />
<br />
 bgcolor="#E0E0E0" April 17<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[#April 17 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 24<br />
 bgcolor="#C6D46E" Wendy Cheng<br />
 bgcolor="#BCE2FE"[[#April 24 Title]]<br />
<br />
 bgcolor="#E0E0E0" May 1<br />
 bgcolor="#C6D46E" Shengyuan Huang<br />
 bgcolor="#BCE2FE"[[#May 1 Orbifold Singular Cohomology]]<br />
}<br />
</center><br />
<br />
== February 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Heisenberg Groups and the Fourier Transform<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE"  Title: DG potpourri<br />
<br />
 bgcolor="#BCD2EE"  Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
<br /><br />
[[File:Dgmeme.pngcenter]]<br />
} <br />
</center><br />
<br />
== February 20 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Completions of Noncatenary Local Domains and UFDs<br />
<br />
 bgcolor="#BCD2EE"  Abstract: A ring is called catenary if for any pair of prime ideals P contained in Q, all saturated chains of prime ideals between P and Q have the same length.<br />
In this talk, I will introduce the necessary background about noncatenary rings and completions of local (Noetherian) domains, as well as the relevant history. Then, I will give the characterization of completions of noncatenary local domains and noncatenary local UFDs, which I will use to describe examples of very strange rings.<br />
} <br />
</center><br />
<br />
== February 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Sun Woo Park'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Baker's Theorem<br />
<br />
 bgcolor="#BCD2EE"  Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
<br /><br />
[[File:Sun_woo_baker.png500pxcenter]]<br />
} <br />
</center><br />
<br />
== March 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Connor Simpson'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Mason's Conjectures and Chow Rings of Matroids<br />
<br />
 bgcolor="#BCD2EE"  Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Dial M_1,1 for moduli<br />
<br />
 bgcolor="#BCD2EE"  Abstract: We will speculate wildly about what kind of object the moduli space of elliptic curves should be. I don't know what a stack is, and I promise not to try to define one.<br />
} <br />
</center><br />
<br />
== March 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract:<br />
} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Colin Crowley'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Alex Hof'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
<br />
[[File:Badromancehof.png500pxcenter]]<br />
} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Name'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Shengyuan Huang'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Orbifold Singular Cohomology<br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=17074Graduate Algebraic Geometry Seminar20190301T19:35:42Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2019 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 6<br />
 bgcolor="#C6D46E" Vlad Sotirov<br />
 bgcolor="#BCE2FE"[[#February 6 Heisenberg Groups and the Fourier Transform]]<br />
<br />
 bgcolor="#E0E0E0" February 13<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[#February 13 DG potpourri]]<br />
<br />
 bgcolor="#E0E0E0" February 20<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[#February 20 Completions of Noncatenary Local Domains and UFDs]]<br />
<br />
 bgcolor="#E0E0E0" February 27<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[#February 27 Baker’s Theorem]]<br />
<br />
 bgcolor="#E0E0E0" March 6<br />
 bgcolor="#C6D46E" Connor Simpson<br />
 bgcolor="#BCE2FE"[[#March 6 Mason's Conjectures and Chow Rings of Matroids]]<br />
<br />
 bgcolor="#E0E0E0" March 13<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[#March 13 Dial M_1,1 for moduli]]<br />
<br />
 bgcolor="#E0E0E0" March 27<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[#March 27 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 3<br />
 bgcolor="#C6D46E" Colin Crowley<br />
 bgcolor="#BCE2FE"[[#April 3 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 10<br />
 bgcolor="#C6D46E" Alex Hof<br />
 bgcolor="#BCE2FE"[[#April 10 Kindergarten GAGA]]<br />
<br />
 bgcolor="#E0E0E0" April 17<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[#April 17 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 24<br />
 bgcolor="#C6D46E" Wendy Cheng<br />
 bgcolor="#BCE2FE"[[#April 24 Title]]<br />
<br />
 bgcolor="#E0E0E0" May 1<br />
 bgcolor="#C6D46E" Shengyuan Huang<br />
 bgcolor="#BCE2FE"[[#May 1 Orbifold Singular Cohomology]]<br />
}<br />
</center><br />
<br />
== February 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Heisenberg Groups and the Fourier Transform<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE"  Title: DG potpourri<br />
<br />
 bgcolor="#BCD2EE"  Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
<br /><br />
[[File:Dgmeme.pngcenter]]<br />
} <br />
</center><br />
<br />
== February 20 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Completions of Noncatenary Local Domains and UFDs<br />
<br />
 bgcolor="#BCD2EE"  Abstract: A ring is called catenary if for any pair of prime ideals P contained in Q, all saturated chains of prime ideals between P and Q have the same length.<br />
In this talk, I will introduce the necessary background about noncatenary rings and completions of local (Noetherian) domains, as well as the relevant history. Then, I will give the characterization of completions of noncatenary local domains and noncatenary local UFDs, which I will use to describe examples of very strange rings.<br />
} <br />
</center><br />
<br />
== February 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Sun Woo Park'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Baker's Theorem<br />
<br />
 bgcolor="#BCD2EE"  Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
<br /><br />
[[File:Sun_woo_baker.png500pxcenter]]<br />
} <br />
</center><br />
<br />
== March 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Connor Simpson'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Mason's Conjectures and Chow Rings of Matroids<br />
<br />
 bgcolor="#BCD2EE"  Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Dial M_1,1 for moduli<br />
<br />
 bgcolor="#BCD2EE"  Abstract: We will speculate wildly about what kind of object the moduli space of elliptic curves should be. I don't know what a stack is, and I promise not to try to define one.<br />
} <br />
</center><br />
<br />
== March 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract:<br />
} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Colin Crowley'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Alex Hof'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
<br />
[[File:Badromancehof.png500pxcenter]]<br />
} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Name'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Shengyuan Huang'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Orbifold Singular Cohomology<br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
[https://www.math.wisc.edu/~moises/ Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=File:Badromancehof.png&diff=17073File:Badromancehof.png20190301T19:34:01Z<p>Moises: Pictorial abstract for Alexander Hof's talk on GAGA</p>
<hr />
<div>Pictorial abstract for Alexander Hof's talk on GAGA</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=17063Graduate Algebraic Geometry Seminar20190228T00:33:59Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2019 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 6<br />
 bgcolor="#C6D46E" Vlad Sotirov<br />
 bgcolor="#BCE2FE"[[#February 6 Heisenberg Groups and the Fourier Transform]]<br />
<br />
 bgcolor="#E0E0E0" February 13<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[#February 13 DG potpourri]]<br />
<br />
 bgcolor="#E0E0E0" February 20<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[#February 20 Completions of Noncatenary Local Domains and UFDs]]<br />
<br />
 bgcolor="#E0E0E0" February 27<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[#February 27 Baker’s Theorem]]<br />
<br />
 bgcolor="#E0E0E0" March 6<br />
 bgcolor="#C6D46E" Connor Simpson<br />
 bgcolor="#BCE2FE"[[#March 6 Mason's Conjectures and Chow Rings of Matroids]]<br />
<br />
 bgcolor="#E0E0E0" March 13<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[#March 13 Dial M_1,1 for moduli]]<br />
<br />
 bgcolor="#E0E0E0" March 27<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[#March 27 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 3<br />
 bgcolor="#C6D46E" Colin Crowley<br />
 bgcolor="#BCE2FE"[[#April 3 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 10<br />
 bgcolor="#C6D46E" Alex Hof<br />
 bgcolor="#BCE2FE"[[#April 10 Kindergarten GAGA]]<br />
<br />
 bgcolor="#E0E0E0" April 17<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[#April 17 Title]]<br />
<br />
 bgcolor="#E0E0E0" April 24<br />
 bgcolor="#C6D46E" Wendy Cheng<br />
 bgcolor="#BCE2FE"[[#April 24 Title]]<br />
<br />
 bgcolor="#E0E0E0" May 1<br />
 bgcolor="#C6D46E" Shengyuan Huang<br />
 bgcolor="#BCE2FE"[[#May 1 Orbifold Singular Cohomology]]<br />
}<br />
</center><br />
<br />
== February 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Heisenberg Groups and the Fourier Transform<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE"  Title: DG potpourri<br />
<br />
 bgcolor="#BCD2EE"  Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
<br /><br />
[[File:Dgmeme.pngcenter]]<br />
} <br />
</center><br />
<br />
== February 20 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Completions of Noncatenary Local Domains and UFDs<br />
<br />
 bgcolor="#BCD2EE"  Abstract: A ring is called catenary if for any pair of prime ideals P contained in Q, all saturated chains of prime ideals between P and Q have the same length.<br />
In this talk, I will introduce the necessary background about noncatenary rings and completions of local (Noetherian) domains, as well as the relevant history. Then, I will give the characterization of completions of noncatenary local domains and noncatenary local UFDs, which I will use to describe examples of very strange rings.<br />
} <br />
</center><br />
<br />
== February 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Sun Woo Park'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Baker's Theorem<br />
<br />
 bgcolor="#BCD2EE"  Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
<br /><br />
[[File:Sun_woo_baker.png500pxcenter]]<br />
} <br />
</center><br />
<br />
== March 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Connor Simpson'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Mason's Conjectures and Chow Rings of Matroids<br />
<br />
 bgcolor="#BCD2EE"  Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Dial M_1,1 for moduli<br />
<br />
 bgcolor="#BCD2EE"  Abstract: We will speculate wildly about what kind of object the moduli space of elliptic curves should be. I don't know what a stack is, and I promise not to try to define one.<br />
} <br />
</center><br />
<br />
== March 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract:<br />
} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Colin Crowley'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Alex Hof'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Name'''<br />
<br />
 bgcolor="#BCD2EE"  Title: <br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Shengyuan Huang'''<br />
<br />
 bgcolor="#BCD2EE"  Title: Orbifold Singular Cohomology<br />
<br />
 bgcolor="#BCD2EE"  Abstract: <br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
[https://www.math.wisc.edu/~moises/ Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2016&diff=17062Graduate Algebraic Geometry Seminar Spring 201620190228T00:32:00Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B139<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
If there is a subject or a paper which you'd like to see someone give a talk on, add it to this list. If you want to give a talk and can't find a topic, try one from this list.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
* A careful explanation of the correspondence between graded modules and sheaves on projective varieties.<br />
<br />
* Braverman and Bezrukavnikov: geometric Langlands correspondence for Dmodules in prime characteristic: the GL(n) case (Note: this title sounds tough but prime characteristic makes things ''easier'')<br />
<br />
* Homological projective duality<br />
<br />
* The orbit method (for classifying representations of a Lie group)<br />
<br />
* Kaledin: geometry and topology of symplectic resolutions<br />
<br />
* Kashiwara: Dmodules and representation theory of Lie groups (Note: Check out that diagram on page 2!)<br />
<br />
* Geometric complexity theory, maybe something like arXiv:1508.05788.<br />
<br />
__NOTOC__<br />
<br />
== Spring 2016 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" January 20<br />
 bgcolor="#C6D46E" Jay Yang<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#January 20 Tropical Geometry II]]<br />
<br />
 bgcolor="#E0E0E0" January 27<br />
 bgcolor="#C6D46E" Jay Yang<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#January 27 Tropical Geometry III ]]<br />
<br />
 bgcolor="#E0E0E0" February 3<br />
 bgcolor="#C6D46E" Ed Dewey<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 3 Derived Category of Projective Space ]]<br />
<br />
 bgcolor="#E0E0E0" February 10 <br />
 bgcolor="#C6D46E" Ed Dewey<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 10 More Derived Category of Projective Space ]] <br />
<br />
 bgcolor="#E0E0E0" February 17<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 17 TBD ]] <br />
<br />
 bgcolor="#E0E0E0" February 24<br />
 bgcolor="#C6D46E" Juliette Bruce<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 24 Divisors and Stuff I]] <br />
<br />
 bgcolor="#E0E0E0" March 2<br />
 bgcolor="#C6D46E" Juliette Bruce<br />
 bgcolor="#BCE2FE" [[Graduate Algebraic Geometry Seminar#March 2 Divisors and Stuff II]] <br />
<br />
 bgcolor="#E0E0E0" March 9<br />
 bgcolor="#C6D46E" Juliette Bruce<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 9 Divisors and Stuff III]] <br />
<br />
 bgcolor="#E0E0E0" March 16<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 16 TBD]] <br />
<br />
 bgcolor="#E0E0E0" March 23<br />
 bgcolor="#C6D46E" N/A<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 23 No GAGS This Week ]] <br />
<br />
 bgcolor="#E0E0E0" March 30<br />
 bgcolor="#C6D46E" Daniel Hast<br />
 bgcolor="#BCE2FE" [[Graduate Algebraic Geometry Seminar#March 30 Jacobians, path integrals, and fundamental groups of curves I]] <br />
<br />
 bgcolor="#E0E0E0" April 6<br />
 bgcolor="#C6D46E" Daniel Hast<br />
 bgcolor="#BCE2FE" [[Graduate Algebraic Geometry Seminar#April 6 Jacobians, path integrals, and fundamental groups of curves II]] <br />
<br />
 bgcolor="#E0E0E0" April 13<br />
 bgcolor="#C6D46E" Jason Steinberg<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 13Something Something Shimura Varieties ]] <br />
<br />
 bgcolor="#E0E0E0" April 20<br />
 bgcolor="#C6D46E" Quinton Westrich<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 20 Projective Duality ]] <br />
<br />
 bgcolor="#E0E0E0" April 27<br />
 bgcolor="#C6D46E" Zachary Charles<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 27 Polynomial systems, toric geometry, and Newton polytopes]] <br />
<br />
 bgcolor="#E0E0E0" May 4<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#May 4 TBD ]] <br />
<br />
 bgcolor="#E0E0E0" May 11<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#May 11 TBD ]] <br />
}<br />
</center><br />
<br />
== January 20 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Jay Yang'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Tropical Geometry II<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: Previously we discussed the basic definitions of tropical geometry, and<br />
the connection to algebraic geometry. Now we use this to count curves<br />
through points on P^2. This is a well known result initially proven<br />
without the use of tropical tools. But using tropical tools we can give<br />
a proof that relies on the combinatorics of lattice paths. I will begin<br />
with a review of some facts from tropical geometry that we need for this<br />
proof. <br />
} <br />
</center><br />
<br />
== January 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
} <br />
</center><br />
== February 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Ed Dewey'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Derived Category of Projective Space<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will talk about the derived category of projective space, covering mostly the same material that Andrei did at the end of his homological algebra course, but at a more leisurely pace. My main reference is the ''Skimming.'' <br />
}<br />
</center><br />
<br />
== February 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Ed Dewey'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: More Derived Category of Projective Space<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will explain in what sense we now "know" the derived category of projective space from Beilinson's result. There is a very nice answer in terms of quivers but I got distracted by another, much less efficient but maybe more flexible approach using dg categories, so that is what we will do. If my understanding permits, we will also talk about the derived category of a projective space bundle.<br />
} <br />
</center><br />
<br />
== February 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD <br />
} <br />
</center><br />
== February 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Juliette Bruce'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Divisors and Stuff I<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
<br />
} <br />
</center><br />
<br />
== March 2 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Juliette Bruce'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Divisors and Stuff II<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
} <br />
</center><br />
<br />
== March 9 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Juliette Bruce'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Divisors and Stuff III<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
} <br />
</center><br />
<br />
== March 16 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
<br />
} <br />
</center><br />
<br />
== March 23 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''No Seminar This Week'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: N/A<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: Enjoy your break!<br />
} <br />
</center><br />
<br />
== March 30 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Daniel Hast'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Jacobians, path integrals, and fundamental groups of curves I<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
} <br />
</center><br />
<br />
== April 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Daniel Hast'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Jacobians, path integrals, and fundamental groups of curves II<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
} <br />
</center><br />
<br />
== April 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Jason Steinberg '''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Something Something Shimura Varieties<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
} <br />
</center><br />
<br />
== April 20 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Quinton Westrich'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Projective Duality<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: Intro to discriminants and duals of projective varieties. My field will be C.<br />
} <br />
</center><br />
<br />
== April 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Zachary Charles'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Polynomial systems, toric geometry, and Newton polytopes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: While the Bezout bound generically gives us the number of roots of a polynomial system in projective space, often much more can be said about specific systems in affine space. Kushnirenko's Theorem (and later Bernstein's theorem) gives better bounds for "sparse" systems of polynomials. These bounds are based on the volume of Newton polytopes. I will prove Kushnirenko's theorem using ideas from toric geometry, commutative algebra, and the geometry of polytopes. If time permits we will give applications of this theorem to power systems.<br />
} <br />
</center><br />
<br />
== May 4 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
} <br />
</center><br />
== May 11 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[http://www.math.wisc.edu/~dewey/ Ed Dewey]<br />
<br />
== Past Semesters ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2016&diff=17061Graduate Algebraic Geometry Seminar Fall 201620190228T00:30:52Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B321 (Updated Fall 2016)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
* David Mumford "Picard Groups of Moduli Problems" (an early paper delving into the geometry of algebaric stacks)<br />
<br />
__NOTOC__<br />
<br />
== Fall 2016 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 14<br />
 bgcolor="#C6D46E" Juliette Bruce<br />
 bgcolor="#BCE2FE"[[#September 14 Vignettes in Algebraic Geometry]]<br />
<br />
 bgcolor="#E0E0E0" September 21<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[#September 21  Hilbert's 21 and The RiemannHilbert correspondence ]]<br />
<br />
 bgcolor="#E0E0E0" September 28<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[#September 28  Hilbert's 21 and The RiemannHilbert correspondence ]]<br />
<br />
 bgcolor="#E0E0E0" October 5 <br />
 bgcolor="#C6D46E" Research Computing in Algebra<br />
 bgcolor="#BCE2FE"[[#October 5 No Seminar Today. ]] <br />
<br />
 bgcolor="#E0E0E0" October 12<br />
 bgcolor="#C6D46E" Nathan Clement<br />
 bgcolor="#BCE2FE"[[#October 12 Spectral Curves and Higgs Bundles ]] <br />
<br />
 bgcolor="#E0E0E0" October 19<br />
 bgcolor="#C6D46E" Nathan Clement<br />
 bgcolor="#BCE2FE"[[#October 19 Spectral Curves and Blowups ]] <br />
<br />
 bgcolor="#E0E0E0" October 26<br />
 bgcolor="#C6D46E" Andrei Caldararu<br />
 bgcolor="#BCE2FE" [[#October 26  What is Mirror Symmetry?]] <br />
<br />
 bgcolor="#E0E0E0" November 2<br />
 bgcolor="#C6D46E" Daniel Erman<br />
 bgcolor="#BCE2FE"[[#November 2 Deformation Theory ]] <br />
<br />
 bgcolor="#E0E0E0" November 9<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[#November 9 Quasicoherent Sheaves and Saturation]] <br />
<br />
 bgcolor="#E0E0E0" November 16<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[#November 16 Gonality of modular curves in characteristic p ]] <br />
<br />
 bgcolor="#E0E0E0" November 23<br />
 bgcolor="#C6D46E" n/a<br />
 bgcolor="#BCE2FE" [[#November 23 No Seminar]] <br />
<br />
 bgcolor="#E0E0E0" November 30<br />
 bgcolor="#C6D46E" n/a<br />
 bgcolor="#BCE2FE" [[#November 30 No Seminar]] <br />
<br />
 bgcolor="#E0E0E0" December 7<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[#December 7 Generic Freeness and the Dimension of Fibres ]] <br />
<br />
 bgcolor="#E0E0E0" December 14<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[#December 14 TBD ]] <br />
}<br />
</center><br />
<br />
== September 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''DJ Bruce'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Vignettes In Algebraic Geometry<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Algebraic geometry is a massive forest, and it is often easy to become lost in the thicket of technical detail and seemingly endless abstraction. The goal of this talk is to take a step back out of these weeds, and return to our roots as algebraic geometers. By looking at three different classical problems we will explore various parts of algebraic geometry, and hopefully motivate the development of some of its larger machinery. Each problem will slowly build with no prerequisite assumed of the listener in the beginning. <br />
} <br />
</center><br />
<br />
== September 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hilbert's 21 and The RiemannHilbert correspondence<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: Enough with the algebra! Away with the schemes and categories! Consider a differential equation with some singularities, such as y'=1/x. Analysis tells us that its solutions can be extended along paths on the complex plane, but when a path loops around the singular point, 0 in this case, the solution might change. This phenomenon is called monodromy. Hilbert's twentyfirst problem asks about the possible inverse of the monodromy construction: if some monodromy is prescribed on the plane with some points removed, is there a nice (Fuchsian), linear differential equation whose solutions have this monodromy? Attempting to solve this problem will quickly take us back to our cozy algebraic geometry world of sheaves and vector bundles. For those of us to whom the word sheaves produces a cold sweat running down our backs, this topic is a great way to motivate and introduce sheaves, and will ultimately give us a reason to care about nontrivial vector bundles.<br />
<br />
No knowledge (or ignorance) of sheaves is required and the analysis in the talk will be contained in the tiny amount that I myself know.<br />
} <br />
</center><br />
<br />
== September 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hilbert's 21 and The RiemannHilbert correspondence<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: Enough with the algebra! Away with the schemes and categories! Consider a differential equation with some singularities, such as y'=1/x. Analysis tells us that its solutions can be extended along paths on the complex plane, but when a path loops around the singular point, 0 in this case, the solution might change. This phenomenon is called monodromy. Hilbert's twentyfirst problem asks about the possible inverse of the monodromy construction: if some monodromy is prescribed on the plane with some points removed, is there a nice (Fuchsian), linear differential equation whose solutions have this monodromy? Attempting to solve this problem will quickly take us back to our cozy algebraic geometry world of sheaves and vector bundles. For those of us to whom the word sheaves produces a cold sweat running down our backs, this topic is a great way to motivate and introduce sheaves, and will ultimately give us a reason to care about nontrivial vector bundles.<br />
<br />
No knowledge (or ignorance) of sheaves is required and the analysis in the talk will be contained in the tiny amount that I myself know.<br />
} <br />
</center><br />
<br />
== October 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''No Talk This Week'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Research Computing in Algebra<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: This weeks seminar conflicts with the "Research Computing in Algebra" workshop, and so instead we will not be having seminar this week. Instead we encourage everyone  but especially those with little computational experience  to go and learn how computation plays a major role in the research of your algebra peers, and how you can begin to integrate computation into your own research. Contact Steve Goldstein for more information.<br />
} <br />
</center><br />
<br />
== October 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Nathan Clement'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Spectral Curves and Higgs Bundles<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
I will present some of the backround motivation for the study of Higgs Bundles, mainly pertaining to Nigel Hitchen's 1987 paper. I will then introduce the spectral curve associated to an operator and describe the relevant geometry.<br />
} <br />
</center><br />
<br />
== October 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Nathan Clement'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Spectral Curves and Blowups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
Continuing on from last time, I will now take a closer look at the geometry of the spectral curve. The main construction will be the lifting of a spectral curve to a blow up of the ambient surface, and the main tool for studying the geometry of this new spectral curve will be intersection theory in a surface.<br />
} <br />
</center><br />
<br />
== October 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Andrei Caldararu'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: What is Mirror Symmetry?<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: Mirror Symmetry is a surprising discovery made in physics around 1992. Its main initial statement was the conjecture that one can calculate certain enumerative invariants (curve counts) on a CalabiYau threefolds by carying out an apparently unrelated calculation (solving a differential equation) related to a very different CalabiYau threefold. Later, two mathematical explanations of mirror symmetry were proposed, one algebraic by Maxim Kontsevich (Homological Mirror Symmetry) and one geometric by StromingerYauZaslow.<br />
} <br />
</center><br />
<br />
== November 2 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Daniel Erman'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Deformation Theory<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: Deformation Theory, What does it know? Does it know things? Let's find out!<br />
} <br />
</center><br />
<br />
== November 9 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Quasicoherent Sheaves and Saturation<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: Given a module, one can form a quasicoherent sheaf on an affine scheme. In much the same way, we can get a quasicoherent sheaf on a projective scheme from any graded module. Unlike in the affine case, this construction fails to give an equivalence of categories. We will examine this construction and explore how saturation can fix this problem.<br />
} <br />
</center><br />
<br />
== November 16 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Wanlin Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Gonality of modular curves in characteristic p<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: My talk is based on Bjorn Poonen's paper with this title. He gave a proof of given a bound on gonality, there are only finitely many modular curves in characteristic p. The same result for characteristic 0 was given by Abramovich in 1966. I will sketch the proof in this talk. This paper used Technics from both number theory and algebraic geometry. <br />
} <br />
</center><br />
<br />
== November 23 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''No Seminar This Week'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Enjoy Thanksgiving!<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: n/a<br />
} <br />
</center><br />
<br />
== November 30 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
} <br />
</center><br />
<br />
== December 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Generic Freeness and the Dimension of Fibres <br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: The fact that the image of a projective variety is closed was known in some special cases as early as Newton, who gave ingenious methods for computing equations of the image (by hand!!). There is no need, though, to ask only about the set of positivedimensional fibres; somewhat more generally, and under very modest assumptions about the schemes in question, the dimension of fibres is semicontinuous on the source (i.e. only jumps up). Guided carefully by David Eisenbud, we begin by proving the generic freeness lemma of Grothendieck and then pass on to the thoroughly lovely Chevalley's Theorem. After accepting a few basic facts about dimension (plus more theorems), our pastoral traipse through the domain of commutative algebra will be basically selfcontained. <br />
} <br />
</center><br />
<br />
== December 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2017&diff=17060Graduate Algebraic Geometry Seminar Spring 201720190228T00:28:33Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' YOU!!<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
<br />
<br />
<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:djbruce@math.wisc.edu DJ], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" January 25<br />
 bgcolor="#C6D46E" Nathan Clement<br />
 bgcolor="#BCE2FE"[[#January 25  Hodge to de Rham, part one]]<br />
<br />
 bgcolor="#E0E0E0" February 1<br />
 bgcolor="#C6D46E" Nathan Clement<br />
 bgcolor="#BCE2FE"[[#February 1  Hodge to de Rham, part two]]<br />
<br />
 bgcolor="#E0E0E0" February 8 <br />
 bgcolor="#C6D46E" Dima Arinkin<br />
 bgcolor="#BCE2FE"[[#February 8  Motivated introduction to geometric Langlands]] <br />
<br />
 bgcolor="#E0E0E0" February 15<br />
 bgcolor="#C6D46E" No Talk<br />
 bgcolor="#BCE2FE"[[#February 15  We Failed, We All Failed]] <br />
<br />
 bgcolor="#E0E0E0" February 22<br />
 bgcolor="#C6D46E" No Talk<br />
 bgcolor="#BCE2FE" [[#February 22  We Failed, We All Failed Pt. 2]] <br />
<br />
 bgcolor="#E0E0E0" March 1<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE" [[#March 1  An Introduction to Mori's Program]] <br />
<br />
 bgcolor="#E0E0E0" March 8<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE" [[#March 8 Picard groups of moduli problems]] <br />
<br />
 bgcolor="#E0E0E0" March 15<br />
 bgcolor="#C6D46E" No Talk<br />
 bgcolor="#BCE2FE" [[#March 15 We Failed, We All Failed Pt. 3]] <br />
<br />
 bgcolor="#E0E0E0" March 22<br />
 bgcolor="#C6D46E" Spring Break<br />
 bgcolor="#BCE2FE" [[#March 22  No Seminar. ]] <br />
<br />
 bgcolor="#E0E0E0" March 29<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE" [[#March 29 Picard groups of moduli problems II]] <br />
<br />
 bgcolor="#E0E0E0" April 5<br />
 bgcolor="#C6D46E" John WiltshireGordon<br />
 bgcolor="#BCE2FE" [[#April 5 Adjoint functors rule your life]] <br />
<br />
 bgcolor="#E0E0E0" April 12<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[#April 12 TBD]] <br />
<br />
 bgcolor="#E0E0E0" April 19<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[#April 19 TBD ]] <br />
<br />
 bgcolor="#E0E0E0" April 26<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[#April 26 A gentle introduction to descent ]] <br />
<br />
 bgcolor="#E0E0E0" May 3<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[#April 26 A gentle introduction to descent, part 2 ]] <br />
}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Nathan Clement'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge to de Rham, part one<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will use the magic of differential calculus in positive characteristic to prove an important result in the cohomology of smooth varieties in positive characteristic. The techniques I'll use are mainly elementary, but prior experience with differential forms, the Frobenius homomorphism, and a little homological algebra will help. This is the setup, come back next week for the punchline!<br />
} <br />
</center><br />
<br />
== February 1 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Nathan Clement'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge to de Rham, part two<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: Having proved an important result in positive characteristic, I'll give a nifty argument to leverage the positive characteristic statement into a characteristic zero result. I'll talk about some cohomology comparison theorems, and we'll see that all this business in positive characteristic provides an alternate proof to the classic Hodge decomposition theorem for cohomology.<br />
} <br />
</center><br />
<br />
== February 8 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Dima Arinkin'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Motivated introduction to geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: The Langlands program originated from bold conjectures formulated by Robert Langlands in the late 1960's. The conjectures <br />
combine number theory and representation theory in a highly unexpected way. The geometric Langlands program adds algebro<br />
geometric methods (and, sometimes, physics) to the mix.<br />
<br />
This interplay of ideas creates a beautiful picture... and a very challenging subject. In my talk, I will suggest one possible <br />
way to approach the area. I plan to focus on questions rather than answers: the goal is to explain how (some of) the questions fit together,<br />
and to tell you the keywords that go into the answers. <br />
} <br />
</center><br />
<br />
== February 15 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''No Talk'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: We Failed, We All Failed Pt. 1<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: n/a<br />
} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''No Talk'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: We Failed, We All Failed Pt. 2<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: n/a<br />
} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Introduction to Mori's Program<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: In studying the birational classification of varieties, one plan of attack is to construct a "simplest" variety in each birational equivalence class. We will see how this approach gives a full structure theory for surfaces, and investigate what new challenges arise in the case of threefolds.<br />
<br />
} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Picard groups of moduli problems<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: In a pastoral traipse, I will discuss some lower bounds on the time it takes an average adult to drink a medium Frosty from Wendy's, including some results of my own about making these bounds sharp. Time permitting, I will also explain how this theory can be extended to study the ingestion of M&M's, a connection previously unkown.<br />
} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''No Talk'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: We Failed, We All Failed Pt. 3<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: n/a<br />
} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Spring Break'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: No Seminar.<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: n/a<br />
} <br />
</center><br />
<br />
== March 29 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Picard groups of moduli problems II<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: Having discussed Grothendieck topologies and an existence theorem for absolute products of families, we construct <math>\mathfrak{M}_{1,1}</math><br />
and give a convenient characterization of the line bundles on the moduli problem, finally proving that <math>\mathrm{Pic}(\mathfrak{M}_{1,1})=\mathbb Z/12</math><br />
. Our numinous and mystical journey towards this sublime result will make ample use of Grothendieck's generalized Hilbert 90. Facts you knew about sheaf cohomology of schemes will suddenly materialize in the context of sites.<br />
} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''John WiltshireGordon'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Adjoint functors rule your life<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: This talk is about adjoint functors. We will do examples!<br />
<br />
} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
} <br />
</center><br />
<br />
== April 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBA'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: TBD<br />
} <br />
</center> <br />
<br />
== April 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A gentle introduction to descent<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I'll give an elementary description of descent theory, mostly distilled from reading [https://arxiv.org/abs/math/0412512 Part I] of [http://www.maa.org/press/maareviews/fundamentalalgebraicgeometrygrothendiecksfgaexplained FGA Explained].<br />
<br />
You can find a(n idealized) transcript of this talk and its sequel at [[File:IntroDescent1.pdf]]<br />
} <br />
</center> <br />
<br />
== May 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A gentle introduction to descent, part 2<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I'll continue my elementary description of descent theory.<br />
<br />
You can find a(n idealized) transcript of this talk and its sequel at [[File:IntroDescent1.pdf]]<br />
<br />
<br />
} <br />
</center> <br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=17059Graduate Algebraic Geometry Seminar Fall 201720190228T00:25:40Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:30pm<br />
<br />
'''Where:'''Van Vleck B321 (Fall 2017)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Fall 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 13<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[#September 13 Vector bundles over the projective line]]<br />
<br />
 bgcolor="#E0E0E0" September 20<br />
 bgcolor="#C6D46E" No Talk<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#September 20  Reflecting on signing up for a talk]]<br />
<br />
 bgcolor="#E0E0E0" September 27<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#September 27  Vector bundles over an elliptic curve]]<br />
<br />
 bgcolor="#E0E0E0" October 4<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#October 4  TBD]] <br />
<br />
 bgcolor="#E0E0E0" October 11<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#October 11  TBD]] <br />
<br />
 bgcolor="#E0E0E0" October 18<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#October 18  TBD]] <br />
<br />
 bgcolor="#E0E0E0" October 25<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE" [[Graduate Algebraic Geometry Seminar Fall 2017#October 25  TBD]] <br />
<br />
 bgcolor="#E0E0E0" November 1<br />
 bgcolor="#C6D46E" Michael Brown<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#November 1  A Theorem of Orlov]] <br />
<br />
 bgcolor="#E0E0E0" November 8<br />
 bgcolor="#C6D46E" Michael Brown<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#November 8  A Theorem or Orlov]] <br />
<br />
 bgcolor="#E0E0E0" November 15<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#November 15  TBD]] <br />
<br />
 bgcolor="#E0E0E0" November 22<br />
 bgcolor="#C6D46E" n/a<br />
 bgcolor="#BCE2FE" [[Graduate Algebraic Geometry Seminar Fall 2017#November 22  No Seminar]] <br />
<br />
 bgcolor="#E0E0E0" November 29<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE" [[Graduate Algebraic Geometry Seminar Fall 2017#November 29  TBD]] <br />
<br />
 bgcolor="#E0E0E0" December 6<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#December 6  What about stacks? ]] <br />
<br />
 bgcolor="#E0E0E0" December 13<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#December 14  What about stacks? II ]] <br />
}<br />
</center><br />
<br />
== September 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Vector Bundles over the projective line<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Next week I will do an overview of Atiyah's classification of bundles on an elliptic curve. Today, I will talk about the tools needed to do this: cohomology of vector bundles. My goal is to keep a loose, islander, Ibizan pace where I will not define anything very rigorously, yet we will get our hands dirty with some computations, not all of which you have sat down and done before (if you have, what is your life? Why am I the one giving this talk?). Our aimless drift will hopefully get us to the much easier classification of vector bundles on the projective line, and we will have achieved the feat of using cohomology to prove a statement that doesn't contain the word cohomology! Flowery crowns are optional.<br />
} <br />
</center><br />
<br />
== September 20 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''No talk'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: You should sign up to give a talk<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== September 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Vector bundles over an elliptic curve<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will regain our continental composture and discuss Atiyah's classification of bundles on an elliptic curve. There will be a ton of preliminary stuff, some lemmas, some theorems and some sketchy proofs. The sun will rise on the east and set on the west, and in the mean time we will learn all the isomorphism classes of vector bundles on an elliptic curve over any field.<br />
<br />
} <br />
</center><br />
<br />
== October 4 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== October 11 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== October 18 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== October 25 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== November 1 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Michael Brown'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A theorem of Orlov<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will discuss the main theorem of Orlov's "Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities". This very powerful theorem provides a comparison between the derived category of coherent sheaves on certain schemes and a related gadget called the "singularity category". Orlov's theorem recovers Beilinson's semiorthogonal decomposition of the bounded derived category of projective space as a special case.<br />
<br />
<br />
} <br />
</center><br />
<br />
== November 8 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Michael Brown'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A Theorem of Orlov<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: This will be a continuation of the previous talk.<br />
<br />
} <br />
</center><br />
<br />
== November 15 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== November 22 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''No Seminar This Week'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Enjoy Thanksgiving!<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: n/a<br />
} <br />
</center><br />
<br />
== November 29 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Nathan Clement'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: What about stacks?<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract:<br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== December 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Nathan Clement'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: What about stacks? II<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2017&diff=17058Graduate Algebraic Geometry Seminar Fall 201720190228T00:24:49Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:30pm<br />
<br />
'''Where:'''Van Vleck B321 (Fall 2017)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
<br />
== Wish List ==<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Fall 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 13<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#September 13 Vector bundles over the projective line]]<br />
<br />
 bgcolor="#E0E0E0" September 20<br />
 bgcolor="#C6D46E" No Talk<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#September 20  Reflecting on signing up for a talk]]<br />
<br />
 bgcolor="#E0E0E0" September 27<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#September 27  Vector bundles over an elliptic curve]]<br />
<br />
 bgcolor="#E0E0E0" October 4<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#October 4  TBD]] <br />
<br />
 bgcolor="#E0E0E0" October 11<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#October 11  TBD]] <br />
<br />
 bgcolor="#E0E0E0" October 18<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#October 18  TBD]] <br />
<br />
 bgcolor="#E0E0E0" October 25<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE" [[Graduate Algebraic Geometry Seminar Fall 2017#October 25  TBD]] <br />
<br />
 bgcolor="#E0E0E0" November 1<br />
 bgcolor="#C6D46E" Michael Brown<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#November 1  A Theorem of Orlov]] <br />
<br />
 bgcolor="#E0E0E0" November 8<br />
 bgcolor="#C6D46E" Michael Brown<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#November 8  A Theorem or Orlov]] <br />
<br />
 bgcolor="#E0E0E0" November 15<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#November 15  TBD]] <br />
<br />
 bgcolor="#E0E0E0" November 22<br />
 bgcolor="#C6D46E" n/a<br />
 bgcolor="#BCE2FE" [[Graduate Algebraic Geometry Seminar Fall 2017#November 22  No Seminar]] <br />
<br />
 bgcolor="#E0E0E0" November 29<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE" [[Graduate Algebraic Geometry Seminar Fall 2017#November 29  TBD]] <br />
<br />
 bgcolor="#E0E0E0" December 6<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#December 6  What about stacks? ]] <br />
<br />
 bgcolor="#E0E0E0" December 13<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2017#December 14  What about stacks? II ]] <br />
}<br />
</center><br />
<br />
== September 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Vector Bundles over the projective line<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Next week I will do an overview of Atiyah's classification of bundles on an elliptic curve. Today, I will talk about the tools needed to do this: cohomology of vector bundles. My goal is to keep a loose, islander, Ibizan pace where I will not define anything very rigorously, yet we will get our hands dirty with some computations, not all of which you have sat down and done before (if you have, what is your life? Why am I the one giving this talk?). Our aimless drift will hopefully get us to the much easier classification of vector bundles on the projective line, and we will have achieved the feat of using cohomology to prove a statement that doesn't contain the word cohomology! Flowery crowns are optional.<br />
} <br />
</center><br />
<br />
== September 20 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''No talk'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: You should sign up to give a talk<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== September 27 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Vector bundles over an elliptic curve<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will regain our continental composture and discuss Atiyah's classification of bundles on an elliptic curve. There will be a ton of preliminary stuff, some lemmas, some theorems and some sketchy proofs. The sun will rise on the east and set on the west, and in the mean time we will learn all the isomorphism classes of vector bundles on an elliptic curve over any field.<br />
<br />
} <br />
</center><br />
<br />
== October 4 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== October 11 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== October 18 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== October 25 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== November 1 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Michael Brown'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A theorem of Orlov<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will discuss the main theorem of Orlov's "Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities". This very powerful theorem provides a comparison between the derived category of coherent sheaves on certain schemes and a related gadget called the "singularity category". Orlov's theorem recovers Beilinson's semiorthogonal decomposition of the bounded derived category of projective space as a special case.<br />
<br />
<br />
} <br />
</center><br />
<br />
== November 8 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Michael Brown'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A Theorem of Orlov<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: This will be a continuation of the previous talk.<br />
<br />
} <br />
</center><br />
<br />
== November 15 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== November 22 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''No Seminar This Week'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Enjoy Thanksgiving!<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: n/a<br />
} <br />
</center><br />
<br />
== November 29 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 6 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Nathan Clement'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: What about stacks?<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract:<br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== December 13 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Nathan Clement'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: What about stacks? II<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=17057Graduate Algebraic Geometry Seminar Spring 201820190228T00:22:49Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 14<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Spring 2018#February 14 Fun with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 21<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Spring 2018#February 21 <math>\mathcal F</math>un with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 28<br />
 bgcolor="#C6D46E" Dima Arinkin<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Spring 2018#February 28 ODEs: algebraic vs analytic vs formal]]<br />
<br />
 bgcolor="#E0E0E0" March 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Spring 2018#March 7 Topology of Affine Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Spring 2018#March 14 Derived Quot Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 21<br />
 bgcolor="#C6D46E" Mao Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Spring 2018#March 21 D modules in prime characteristic]]<br />
<br />
 bgcolor="#E0E0E0" March 28<br />
 bgcolor="#C6D46E" Spring break<br />
 bgcolor="#BCE2FE" Whoo!<br />
<br />
 bgcolor="#E0E0E0" April 4<br />
 bgcolor="#C6D46E" Rachel Davis<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Spring 2018#April 4 Introduction to Grothendieck's dessins d'enfants]]<br />
<br />
 bgcolor="#E0E0E0" April 11<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Spring 2018#April 11 Néron models of elliptic curves]]<br />
<br />
 bgcolor="#E0E0E0" April 18<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Spring 2018#April 18 Modular forms over arbitrary rings]]<br />
<br />
 bgcolor="#E0E0E0" April 25<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Spring 2018#April 25 The Theory of Heights and the Height of Theories]]<br />
<br />
 bgcolor="#E0E0E0" May 2<br />
 bgcolor="#C6D46E" No talk today<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Spring 2018#May 2 Keith Rush is giving a talk at the same time]]<br />
}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Fun with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
My goal is to next week talk about Gerard Laumon's preprint ''Transformation de Fourier généralisée'', which will encapsulate all the Fourier transforms I can name (which for me includes the Fourier transform for Dmodules on affine space, the Mellin transform, the FourierMukai transform for abelian varieties and the rare John Mahoney transform between modules on the punctured line and vector spaces with a Zaction) into one crazy package.<br />
<br />
In order to achieve this altered mental state, we will have to rethink all our preconceptions, and rediscover algebraic groups, make sense of Cartier duality for them, define formal groups along the way, and see how duality of Abelian varieties relates to Cartier duality. If you come to the talk in an already in this altered mental state, then hopefully I'll do some examples that you've been too lazy to work out for yourself.<br />
<br />
} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''<math>\mathcal F</math>un with commutative groups'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: <math>\mathcal F</math>un with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will talk about how last week's Cartier duality relates to duality for abelian varieties. Then we will see how this allows us to take certain complexes of groups which are self dual, going back to altered mental states which are now derived.<br />
<br />
If we're going to Fourier transform something, it should be a sheaf, but what is even a sheaf on a complex of groups? Once we see what it should be, I will handwave what the Fourier transform is and give a bunch of concrete examples.<br />
<br />
} <br />
</center><br />
<br />
== February 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Dima Arinkin'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: ODEs: algebraic vs analytic vs formal<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Linear ordinary differential equations (or, as they are known geometrically, bundles with connections on Riemann surfaces) can be studied from many directions. In algebraic geometry, the goal is ''to classify'' equations rather than ''to solve'' them. The classification can be<br />
done in different settings: algebraic, analytic, or formal; each setting has its advantages and disadvantages. However, for one of the most<br />
important class of equations (equations with regular singularities aka Fuchsian equations) the three approaches agree, leading to a rich <br />
and beautiful picture. <br />
<br />
In my talk, I will sketch the algebraic theory of differential equations, focusing on equations with regular singularities. (I do not expect to have time<br />
for irregular singularities.) The talk is related to my topics course on Dmodules, but it does not rely on the topics course.<br />
} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Topology of Affine Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will explain in what sense flat morphisms of (affine) schemes are the correct analogue of open maps of topological spaces, and then use that to explain how surjectivity in the sense of Zariski spectra corresponds to surjectivity of functors of points.<br />
<br />
} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Derived Quot Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The titular paper of CiocanFontanine & Kapranov constructs a "derived" version of Grothendieck's Quot scheme, whose degree zero truncation is the ordinary Quot scheme, and whose tangent space at each kpoint consists higher Ext's. In this talk, we will talk about what is meant by "derived" in modern AG and why you might want a derived Quot scheme. In the remaining time, we will give a (hopefully transparent) description of how CF&K construct RQuot.<br />
<br />
} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Mao Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Dmodules in prime characteristic<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The usual theory of Dmodules concerns itself with sheaves and varieties over complex numbers. In this talk I'm going to consider its characteristic p analogue. The new feature is that the ring of differential operators has a large center. By using this extra information we can give a more precise description about the ring of differential operators, namely it has a canonical structure of an Azumaya algebra over the twisted cotangent bundle. This has lots of applications in algebraic geometry and representation theory. <br />
<br />
} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Rachel Davis'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Introduction to Grothendieck's dessins d'enfants<br />
<br />
 bgcolor="#BCD2EE"  <br />
In 1978 Bely&#301; first announced the following theorem: every algebraic curve defined over a fixed algebraic closure of the rationals can be represented as a covering of the projective line ramified over at most three points. Deligne then studied the fundamental group of the projective line minus three points. Grothendieck introduced combinatorial structures called dessins d'enfants. One consequence of Bely&#301;'s theorem is that the Galois action on the fundamental group of the projective line minus three points is faithful. <br />
} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Néron models of elliptic curves<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will attempt to do algebraic geometry over the integers. Doing this for elliptic curves will lead us to the idea of Néron models, and we will see how to get our hands on these guys explicitly.<br />
<br />
} <br />
</center><br />
<br />
== April 18 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Modular forms over arbitrary rings<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
One way to understand moduli spaces of elliptic curves and related moduli problems better, is to study modular forms. With this in mind, I will define modular forms over arbitrary rings in the sense of Katz. I will also talk about padic modular forms in the sense of Serre and hopefully motivate the modern treatment of such modular forms.<br />
<br />
} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: The Theory of Heights and the Height of Theories<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will talk about some of the different notions of height in arithmetic geometry, starting from the most naive, ending at some betterer ones.<br />
<br />
} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Fall_2018&diff=17056Graduate Algebraic Geometry Seminar Fall 201820190228T00:21:54Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Autumn 2018 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#September 12 Linear Resolutions of Edge Ideals]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#September 26 An Elementary Introduction to Geometric Langlands]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#October 3 Gonality of Curves and More]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#October 10 A Gentle introduction to Grothendieck's Galois theory]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#October 17 Schubert Calculus]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#October 24 Quadratic Polynomials]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#October 31 How to Parameterize Elliptic Curves and Influence People]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#November 7 Morita Duality and Local Duality]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#November 14 Homological Projective Duality]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#November 30 Deformation Theory]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#December 5 One Step Closer to <math>B_{cris}</math>]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar Fall 2018#December 12 A Survey of Newton Polygons]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Linear Resolutions of Edge Ideals<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Qiao He'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Elementary Introduction to Geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Wanlin Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Gonality of Curves and More<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Ewan Dalby'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A Gentle introduction to Grothendiecks Galois theory<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Johnnie Han'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Schubert Calculus<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19thcentury Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Quadratic Polynomials<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of Lfunctions to show up, that would be ridiculous.<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: How to Parameterize Elliptic Curves and Influence People<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Morita duality and local duality<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Homological Projective Duality<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics. <br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Asvin G'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Deformation Theory<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will explain what deformation theory is and how to use it by doing a few examples.<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: One Step Closet to <math>B_{cris}</math><br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will talk about various comparison theorems in <math>p</math>adic cohomology, and time permitting, describe the crystalline side of things in greater detail.<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Sun Woo Park'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A Survey of Newton Polygons<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: I will give a survey on how understanding newton polygons can be useful in solving many different problems in algebraic geometry: from the proof of padic Weierstrass Formula to the reformulization of Tate's Algorithm for elliptic curves. (Since I will focus on providing various applications of newton polygons, I will not be able to present rigorous proofs to most of the statements I will make in this talk.)<br />
<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16460Graduate Algebraic Geometry Seminar20181126T21:20:10Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Linear Resolutions of Edge Ideals]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 An Elementary Introduction to Geometric Langlands]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 Gonality of Curves and More]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 A Gentle introduction to Grothendieck's Galois theory]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 Schubert Calculus]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 Quadratic Polynomials]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 How to Parameterize Elliptic Curves and Influence People]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 Morita Duality and Local Duality]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 Homological Projective Duality]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 Picard groups of moduli schemes]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Linear Resolutions of Edge Ideals<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Qiao He'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Elementary Introduction to Geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Wanlin Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Gonality of Curves and More<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Ewan Dalby'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A Gentle introduction to Grothendiecks Galois theory<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Johnnie Han'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Schubert Calculus<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19thcentury Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Quadratic Polynomials<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of Lfunctions to show up, that would be ridiculous.<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: How to Parameterize Elliptic Curves and Influence People<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Morita duality and local duality<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Homological Projective Duality<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics. <br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Asvin Gothandaraman'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Picard groups of moduli schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16402Graduate Algebraic Geometry Seminar20181113T22:36:31Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Linear Resolutions of Edge Ideals]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 An Elementary Introduction to Geometric Langlands]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 Gonality of Curves and More]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 A Gentle introduction to Grothendieck's Galois theory]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 Schubert Calculus]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 Quadratic Polynomials]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 How to Parameterize Elliptic Curves and Influence People]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 Morita Duality and Local Duality]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 Homological Projective Duality]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Linear Resolutions of Edge Ideals<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Qiao He'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Elementary Introduction to Geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Wanlin Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Gonality of Curves and More<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Ewan Dalby'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A Gentle introduction to Grothendiecks Galois theory<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Johnnie Han'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Schubert Calculus<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19thcentury Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Quadratic Polynomials<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of Lfunctions to show up, that would be ridiculous.<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: How to Parameterize Elliptic Curves and Influence People<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Morita duality and local duality<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Homological Projective Duality<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics. <br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16335Graduate Algebraic Geometry Seminar20181104T22:34:15Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Linear Resolutions of Edge Ideals]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 An Elementary Introduction to Geometric Langlands]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 Gonality of Curves and More]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 A Gentle introduction to Grothendieck's Galois theory]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 Schubert Calculus]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 Quadratic Polynomials]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 How to Parameterize Elliptic Curves and Influence People]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 Morita Duality and Local Duality]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Linear Resolutions of Edge Ideals<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Qiao He'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Elementary Introduction to Geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Wanlin Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Gonality of Curves and More<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Ewan Dalby'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A Gentle introduction to Grothendiecks Galois theory<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Johnnie Han'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Schubert Calculus<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19thcentury Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Quadratic Polynomials<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of Lfunctions to show up, that would be ridiculous.<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: How to Parameterize Elliptic Curves and Influence People<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Morita duality and local duality<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract:<br />
<br />
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.<br />
<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16317Graduate Algebraic Geometry Seminar20181030T14:41:47Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Linear Resolutions of Edge Ideals]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 An Elementary Introduction to Geometric Langlands]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 Gonality of Curves and More]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 A Gentle introduction to Grothendieck's Galois theory]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 Schubert Calculus]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 Quadratic Polynomials]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 How to Parameterize Elliptic Curves and Influence People]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov/David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner/Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Linear Resolutions of Edge Ideals<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Qiao He'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Elementary Introduction to Geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Wanlin Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Gonality of Curves and More<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Ewan Dalby'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A Gentle introduction to Grothendiecks Galois theory<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Johnnie Han'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Schubert Calculus<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19thcentury Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Quadratic Polynomials<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of Lfunctions to show up, that would be ridiculous.<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: How to Parameterize Elliptic Curves and Influence People<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
A classical guide to classifying curves for the geomterically minded grad student. I will assume basically zero AG background.<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Math_Circle_de_Madison&diff=16304Math Circle de Madison20181029T22:18:22Z<p>Moises: </p>
<hr />
<div>[[Image:logo.pngright440px]]<br />
<br />
Para ver la página en inglés, visitar [[Madison Math Circle]]<br />
=¿Qué es un Math Circle?=<br />
<br />
El Math Circle de Madison son unas actividades matemáticas semanales (en inglés) dirigidas a alumnos de middle school y de high school que estén interesados. Es un programa de divulgación organizado por el Departamento de Matemáticas de la Universidad de Wisconsin. Nuestro objetivo es dar intuición sobre ideas emocionantes en Matemáticas y Ciencia. En el pasado, hemos tenido charlas sobre plasma y el tiempo en el espacio exterior, gráficos en los videojuegos y encriptación. En las sesiones se les pide a los estudiantes (y a sus padres) que afronten los problemas ellos mismos, mientras el ponente facilita el diálogo. Las charlas son independientes unas de otras, así que nuevos estudiantes son bienvenidos en cualquier momento.<br />
<br />
El nivel del público varía bastante, ya que es una mezcla de estudiantes de middle school y high school, y los conferenciantes suelen afrontar esto optando por temas que sean interesantes para un grupo diverso de estudiantes.<br />
<br />
<br />
[[Image: MathCircle_2.jpg500px]] [[Image: MathCircle_4.jpg500px]] <br />
<br />
Después de cada charla tendremos pizza pagada por el Departamento de Matemáticas, y los estudiantes tendrán la oportunidad de hablar con el ponente y con los otros participantes, hacer preguntas sobre algunos de los temas de los que se haya hablado, y también sobre la universidad, carreras de ciencias, etc.<br />
<br />
'''El Math circle de Madison apareció en el periódico Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/schoolspotlightmadisonmathcirclegivesyoungstudentsataste/article_77f5c0420b3d11e1ba5f001cc4c03286.html ¡mira!]<br />
<br />
=De acuerdo, ¡quiero ir!=<br />
<br />
Nos reunimos semanalmente, <b>los lunes a las 6pm en el aula 3255 de la biblioteca Helen C. White</b>, durante el curso escolar. <b>¡Nuevos estudiantes son bienvenidos en cualquier momento!</b> Es gratis y las charlas son independientes unas de otras, así que puedes venir cualquier semana sin tener que haber hecho ningún trámite previo, pero les pedimos a todos los participantes que dediquen un minuto de su tiempo para registrarse en la siguiente dirección (en inglés):<br />
<br />
[https://uwmadison.co1.qualtrics.com/SE/?SID=SV_0qPme0LEpUi4kZf '''Formulario para registrarse en Math Circle''']<br />
<br />
Toda tu información es privada, y sólo la usa el organizador del Math Circle de Madison para llevar la actividad.<br />
<br />
Si eres un estudiante, esperamos que informes a otros estudiantes interesados sobre estas charlas , y que hables con tus padres o con tu profesor/a para organizar el transporte en coche al campus de la Universidad de Wisconsin. Si eres un padre, una madre, o un profesor/a, esperamos que informes a tus estudiantes sobre estas charlas y que organices el transporte en coche a la universidad (todas las charlas son en el aula 3255 de la biblioteca Helen C. White, en el campus de la Universidad de WisconsinMadison, al lado de Memorial Union).<br />
<br />
<br />
==Dónde estamos/estacionamiento==<br />
Nos reunimos en el tercer piso del edificio Helen C. White, en la habitación 3255.<br />
<br />
<div class="center" style="width:auto; marginleft:auto; marginright:auto;"><br />
[[File: Helencwhitemap.png400px]]</div><br />
<br />
'''Estacionamiento''' El estacionamiento dentro del campus está muy limitado. Aquí damos una lista con algunas otras opciones:<br />
<br />
*Hay un garaje en el sótano de Helen C. White, con una tarifa horaria. Entrar por Park Street.<br />
*Un paseo de 0.5 millas al edificio Helen C. White por [http://goo.gl/cxTzJY estas indicaciones], hay muchas plazas ('''gratis desde las 4:30pm''') [http://goo.gl/maps/Gkx1C en el Lot 26 en Observatory Drive].<br />
*Un paseo de 0.3 millas al edificio Helen C. White por [http://goo.gl/yMJIRd estas indicaciones], hay muchas plazas ('''gratis desde las 4:30pm''') [http://goo.gl/maps/vs17X en el Lot 34].<br />
*Un paseo de 0.3 millas al edificio Helen C. White por [http://goo.gl/yMJIRd estas indicaciones], 2 plazas con parquímetro (máximo 25 minutos) [http://goo.gl/maps/ukTcu delante de Lathrop Hall]<br />
*Un paseo de 0.3 millas al edificio Helen C. White por [http://goo.gl/b8pdk2 estas indicaciones], 6 plazas con parquímetro (máximo 25 minutos) en [http://goo.gl/maps/6EAnc el círculo delante de Chadbourne Hall] .<br />
*Para más información, ver la [http://transportation.wisc.edu/parking/parking.aspx página de información de estacionamiento de UWMadison].<br />
<br />
==Lista de correo==<br />
<br />
La mejor manera de mantenerse actualizado es apuntarse a nuestra lista de correo. Para ello, manda un mensaje vacío a joinmathcircle@lists.wisc.edu<br />
<br />
==Contacta con los organizadores==<br />
El Math Circle de Madison está organizado por tres profesores y tres estudiantes de doctorado del [http://www.math.wisc.edu Departamento de Matemáticas] de la Universidad de WisconsinMadison. Si tienes alguna pregunta o alguna sugerencia de temas para las charlas, escríbenos a [mailto:mathcircleorganizers@lists.wisc.edu esta dirección] (puedes hacerlo en español). ¡Siempre queremos recibir vuestros comentarios!<br />
<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
File:pmwood.jpg[http://www.math.wisc.edu/~pmwood/ Prof. Phillip Matchett Wood]<br />
File:Craciun.jpg[http://www.math.wisc.edu/~craciun/ Prof. Gheorghe Craciun]<br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
File:juliettebruce.jpg[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]<br />
File:Ee.jpg[http://www.math.wisc.edu/~evaelduque/ Eva Elduque]<br />
File:mrjulian.jpg[http://www.math.wisc.edu/~mrjulian/ Ryan Jullian]<br />
<br />
</gallery><br />
</center><br />
<br />
==Donaciones==<br />
<br />
Por favor, considera la posibilidad de donar al Math Circle de Madison. Como decimos en nuestro [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf informe anual], nuestros mayores gastos son la pizza y los materiales que necesitan algunos de los ponentes. Hasta ahora todos nuestros gastos han sido cubiertos por donaciones del Departamento de Matemáticas de UW y por regalos generosos de un donante privado. Pero nuestros gastos están creciendo, sobre todo porque este año esperamos tener más charlas que cualquier otro. De hecho, este año esperamos gastar al menos 2500$ solamente en pizza y materiales.<br />
<br />
Así que por favor, ¡considera la posibilidad de donar para apoyar a tu Math Circle! La manera más sencilla es ir a la dirección:<br />
<br />
[http://www.math.wisc.edu/donate Dirección para donar online]<br />
<br />
En esa página hay instrucciones para donar al Departamento de Matemáticas. <b> ¡Asegúrate de añadir un mensaje diciendo que la donación está destinada al "Madison Math Circle"!</b> El dinero va al Fondo Anual del Departamento de Matemáticas, y pasa por la Fundación de la Universidad de Wisconsin (University of Wisconsin Foundation). Esto hace que este método sea práctico desde el punto de vista de la gestión, etc.<br />
<br />
Como alternativa, también puedes traer un cheque a una de las reuniones del Math Circle. Si traes un cheque, asegúrate que puede ser canjeado por la "WFAA" y añade el comentario "Math Circle Donation" en el cheque.<br />
<br />
Si lo prefieres, también puedes pagar en efectivo, y te daremos un resguardo.<br />
<br />
==¡Ayúdanos a crecer!==<br />
<br />
Si te gusta Math Circle, ¡ayúdanos a seguir creciendo, por favor! Tanto estudiantes como padres y profesores pueden ayudar de las siguientes maneras:<br />
*Enseñando nuestro [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''panfleto'''] en colegios o en cualquier sitio donde pueda haber estudiantes interesados<br />
*Hablando sobre Math Circle con estudiantes, padres, profesores, gestores, y otros<br />
*Informar sobre Math Circle en las reuniones de la PTO (Parent Teacher Organization)<br />
*Donar al Math Circle<br />
<br />
Contacta con los organizadores si tienes alguna pregunta o alguna idea sobre cómo ayudar.<br />
<br />
=Reuniones en Otoño 2015 y Primavera 2016=<br />
<br />
Todas las charlas empiezan a las '''6pm en el aula 3255 de la biblioteca Helen C. White''', salvo que se diga lo contrario.<br />
<br />
La lista completa de fechas, ponentes y sus charlas está en la [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle#Meetings_for_Fall_2015_and_Spring_2016 '''página en inglés'''], que se actualiza semanalmente.<br />
<br />
=Reuniones en High Schools=<br />
<br />
Estamos experimentando con celebrar algunas de nuestras reuniones de Math Circle en High Schools de la zona. Para más información, visitar la [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle#High_School_Meetings '''página en inglés''']<br />
<br />
<br />
=Recursos de utilidad=<br />
==Informes anuales==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf Informe anual de 20132014]<br />
<br />
== Resúmenes de charlas pasadas==<br />
[[Archived Math Circle Material]]<br />
<br />
==Enlaces de interés para los ponentes (en progreso)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Consejos para los ponentes de Math Circle]<br />
<br />
[http://www.mathcircles.org/content/lessonplans Ejemplos de clases]<br />
<br />
[http://www.mathcircles.org/content/circlebox "Circle in a Box"]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Math_Circle_Presentations&diff=16303Math Circle Presentations20181029T22:14:35Z<p>Moises: </p>
<hr />
<div>=Advice on presenting at the Madison Math Circle=<br />
This page is meant as a resource for presenters at the Madison Math Circle.<br />
<br />
==Who is the audience?==<br />
The audience currently consists primarily of middle school students, but there are some high school students and a few advanced elementary school students as well. The number of students has varied somewhat dramatically in recent semesters, but you should expect about 2030 students.<br />
<br />
==Selecting a topic==<br />
Basically any topic with a mathematical or quantitative component could be an appropriate topic. We have seen excellent presentations on: logic puzzles, sorting algorithms, computer graphics, the mathematics of juggling, origami, sine and cosine functions, Catalan numbers, the mathematics of the game Set, and more. One key is crafting problems that the students can explore on their own which will give them a feel for the larger topic. If you want help in fleshing out an idea, contact the organizers! <br />
<br />
The book Circle in a Box by Sam Vandervelde (which is available online http://www.mathcircles.org/node/65 or at our very own math library) has lots of nice ideas.<br />
<br />
==Sample Schedule==<br />
We encourage presenters to spend half of the time having students explore problems on their own. For instance, a common and successful format would like this:<br />
<ul><br />
<li> 6:006:05: Begin the session with a brief introduction of the topic. Setup the first round of problems. </li><br />
<li> 6:056:20: Students work on problems. (Note: if you're presenting on a rich topic, like cryptography or computer graphics, it may be the case the problems only give a taste of the kind of mathematics involved. This is okay!)</li><br />
<li> 6:206:35: Discuss solutions to some of the problems and how they relate to your topic. Set up new problems. </li><br />
<li> 6:356:45: Work on new problems. </li><br />
<li> 6:457:00: Concluding discussion of topic. Discuss some of the directions this type of thinking can lead, maybe including further problems. Pizza arrives around 6:50, so discussion can end at any point between 6:50 and 7:00 depending on how things are going.<br />
</li><br />
</ul><br />
<br />
==AV Equipment==<br />
For computer slides, we encourage you to bring your own laptop (and adapter, if using a Mac). In addition, our experience has been that sometimes computer issues arise with individual laptops, and so to avoid these issues, we will ask that you email a copy of your slides (in PDF or Powerpoint format) to mathcircleorganizers@math.wisc.edu at least 24 hours in advance of your presentation.<br />
<br />
If you would like to use AV equipment for a purpose other than just computer slides, please let us know in advance! We want to make your presentation as seamless as possible.<br />
<br />
<br />
==Supplies==<br />
If you want to include special supplies in your presentation, please let us know as soon as possible. The Madison Math Circle owns some supplies (decks of Set, ???) which will happily lend out. We are also happy to print out worksheets or any other handouts. Finally, we have a limited budget for purchasing other supplies, and we will do our best to accommodate any request.<br />
<br />
==Questions==<br />
If you have any questions at all, you can write directly to any of the organizers (Juliette Bruce, Eva Elduque, Daniel Erman, Ryan Julian, and Soumya Sankar) or you can email the organizers list: mathcircleorganizers@math.wisc.edu.</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=16302Madison Math Circle20181029T22:09:32Z<p>Moises: </p>
<hr />
<div>[[Image:logo.pngright440px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg500px]] [[Image: MathCircle_4.jpg500px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/schoolspotlightmadisonmathcirclegivesyoungstudentsataste/article_77f5c0420b3d11e1ba5f001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UWMadison campus, right next to the Memorial Union).<br />
<br />
<br />
==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; marginleft:auto; marginright:auto;"><br />
[[File: Helencwhitemap.png400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UWMadison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to joinmathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UWMadison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@lists.wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
File:Betsy.jpg[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]<br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
File:juliettebruce.jpg[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]<br />
File:Ee.jpg[http://www.math.wisc.edu/~evaelduque/ Eva Elduque]<br />
File:mrjulian.jpg[http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
File:soumyasankar.jpg[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]<br />
</gallery><br />
</center><br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
<br />
So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for recordkeeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can just pay in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
*Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students<br />
*Discussing the Math Circle with students, parents, teachers, administrators, and others<br />
*Making an announcement about Math Circle at PTO meetings<br />
*Donating to Math Circle<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Meetings for Fall 2018=<br />
<br />
<center><br />
<br />
Unless specified talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
{ style="color:black; fontsize:120%" border="1" cellpadding="14" cellspacing="0"<br />
<br />
! colspan="3" style="background: #e8b2b2;" align="center"  Fall 2018<br />
<br />
! Date !! Speaker !! Topic<br />
<br />
 September 17, 2018  Sun Woo Park  Why are Donuts and Cream Puffs "different"?<br />
<br />
 September 24, 2018  Ben Bruce  Three Cottages Problem<br />
<br />
 October 1, 2018  Kit Newton  How to calculate Pi if all you can do is throw things<br />
<br />
 October 8, 2018  Connor Simpson  TBD<br />
<br />
 October 15, 2018  JeanLuc Thiffeault  TBD<br />
<br />
 October 22, 2018  Patrick Nicodemus  Formal Systems in Computer Science and Logic<br />
<br />
 October 29, 2018  Moisés Herradón Cueto  Order and chaos in population sizes ([http://www.math.wisc.edu/~moises/Math_Circle_Talk.html try it yourself!])<br />
<br />
 November 5, 2018  Christian Geske  Josephus Problem<br />
<br />
 November 12, 2018  Rachel Davis  TBD<br />
<br />
 November 19, 2018  Uri Andrews  King Chicken<br />
<br />
}<br />
<br />
</center><br />
<br />
=OffSite Meetings=<br />
<br />
We will hold some Math Circle meetings at local high schools on early release days. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<br />
<center><br />
<br />
{ style="color:black; fontsize:120%" border="1" cellpadding="14" cellspacing="0"<br />
<br />
! colspan="5" style="background: #e8b2b2;" align="center"  Fall 2017<br />
<br />
<br />
! Date !! Time !! Location !! Speaker !! Topic <br />
<br />
 October 29th  2:45pm East High School  Madison, WI  TBD  TBD <br />
<br />
 December 3rd  2:45pm East High School  Madison, WI  TBD  TBD<br />
<br />
}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 20132014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_20162017 2016  2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_20162017 2016  2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_20152016 2015  2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_20152016 2015  2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_20152016 2015  2015 Abstracts]<br />
<br />
[[Archived Math Circle Material]]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.mathcircles.org/content/lessonplans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circlebox "Circle in a Box"]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16236Graduate Algebraic Geometry Seminar20181021T22:25:25Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Linear Resolutions of Edge Ideals]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 An Elementary Introduction to Geometric Langlands]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 Gonality of Curves and More]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 A Gentle introduction to Grothendieck's Galois theory]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 Schubert Calculus]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 Quadratic Polynomials]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov/David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner/Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Linear Resolutions of Edge Ideals<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Qiao He'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Elementary Introduction to Geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Wanlin Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Gonality of Curves and More<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Ewan Dalby'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A Gentle introduction to Grothendiecks Galois theory<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Johnnie Han'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Schubert Calculus<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 19thcentury Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.<br />
<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Quadratic Polynomials<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of Lfunctions to show up, that would be ridiculous.<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=16224Madison Math Circle20181018T18:42:22Z<p>Moises: </p>
<hr />
<div>[[Image:logo.pngright440px]]<br />
<br />
For the site in Spanish, visit [[Math Circle de Madison]]<br />
=What is a Math Circle?=<br />
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.<br />
<br />
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.<br />
<br />
<br />
[[Image: MathCircle_2.jpg500px]] [[Image: MathCircle_4.jpg500px]] <br />
<br />
<br />
After each talk we'll have pizza provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.<br />
<br />
'''The Madison Math circle was featured in Wisconsin State Journal:''' [http://host.madison.com/wsj/news/local/education/local_schools/schoolspotlightmadisonmathcirclegivesyoungstudentsataste/article_77f5c0420b3d11e1ba5f001cc4c03286.html check it out]!<br />
<br />
=All right, I want to come!=<br />
<br />
We have a weekly meeting, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. <b>New students are welcome at any point! </b> There is no fee and the talks are independent of one another, so you can just show up any week, but we ask all participants to take a moment to register by following the link below:<br />
<br />
[https://uwmadison.co1.qualtrics.com/jfe/form/SV_e9WdAs2SXNurWFD '''Math Circle Registration Form''']<br />
<br />
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the Circle. <br />
<br />
If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus. If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in 3255 Helen C White Library, on the UWMadison campus, right next to the Memorial Union).<br />
<br />
<br />
==Directions and parking==<br />
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.<br />
<br />
<div class="center" style="width:auto; marginleft:auto; marginright:auto;"><br />
[[File: Helencwhitemap.png400px]]</div><br />
<br />
'''Parking.''' Parking on campus is rather limited. Here is as list of some options:<br />
<br />
*There is a parking garage in the basement of Helen C. White, with an hourly rate. Enter from Park Street.<br />
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].<br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. <br />
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].<br />
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .<br />
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UWMadison Parking Info website].<br />
<br />
==Email list==<br />
The best way to keep up to date with the what is going is by signing up for our email list. Send an empty email to joinmathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UWMadison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@lists.wisc.edu here]. We are always interested in feedback!<br />
<center><br />
<gallery widths=480px heights=240px mode="packed"><br />
File:de.jpg[https://www.math.wisc.edu/~derman/ Prof. Daniel Erman]<br />
File:Betsy.jpg[http://www.math.wisc.edu/~stovall/ Prof. Betsy Stovall]<br />
</gallery><br />
<br />
<gallery widths=500px heights=250px mode="packed"><br />
File:juliettebruce.jpg[http://www.math.wisc.edu/~juliettebruce/ Juliette Bruce]<br />
File:Ee.jpg[http://www.math.wisc.edu/~evaelduque/ Eva Elduque]<br />
File:mrjulian.jpg[http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
File:soumyasankar.jpg[http://www.math.wisc.edu/~soumyasankar Soumya Sankar]<br />
</gallery><br />
</center><br />
<br />
==Donations==<br />
Please consider donating to the Madison Math Circle. As noted in our [https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf annual report], our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from a private donor. But our costs are rising, primarily because this year we expect to hold more meetings than in any previous year. In fact, this year, we expect to spend at least $2500 on pizza and supplies alone.<br />
<br />
So please consider donating to support your math circle! The easiest way to donate is to go to the link:<br />
<br />
[http://www.math.wisc.edu/donate Online Donation Link]<br />
<br />
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b> The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for recordkeeping, etc.<br />
<br />
Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. <br />
<br />
Or you can just pay in cash, and we'll give you a receipt.<br />
<br />
==Help us grow!==<br />
If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:<br />
*Posting our [https://www.math.wisc.edu/wiki/images/MMC_Flyer_2016.pdf '''flyer'''] at schools or anywhere that might have interested students<br />
*Discussing the Math Circle with students, parents, teachers, administrators, and others<br />
*Making an announcement about Math Circle at PTO meetings<br />
*Donating to Math Circle<br />
Contact the organizers if you have questions or your own ideas about how to help out.<br />
<br />
=Meetings for Fall 2018=<br />
<br />
<center><br />
<br />
Unless specified talks start at '''6pm in room 3255 of Helen C. White Library''', unless otherwise noted.<br />
<br />
{ style="color:black; fontsize:120%" border="1" cellpadding="14" cellspacing="0"<br />
<br />
! colspan="3" style="background: #e8b2b2;" align="center"  Fall 2018<br />
<br />
! Date !! Speaker !! Topic<br />
<br />
 September 17, 2018  Sun Woo Park  Why are Donuts and Cream Puffs "different"?<br />
<br />
 September 24, 2018  Ben Bruce  Three Cottages Problem<br />
<br />
 October 1, 2018  Kit Newton  How to calculate Pi if all you can do is throw things<br />
<br />
 October 8, 2018  Connor Simpson  TBD<br />
<br />
 October 15, 2018  JeanLuc Thiffeault  TBD<br />
<br />
 October 22, 2018  Patrick Nicodemus  TBD<br />
<br />
 October 29, 2018  Moisés Herradón Cueto  Order and chaos in population sizes (mostly chaos)<br />
<br />
 November 5, 2018  Christian Geske  Josephus Problem<br />
<br />
 November 12, 2018  TBD  TBD<br />
<br />
 November 19, 2018  TBD  TBD<br />
<br />
}<br />
<br />
</center><br />
<br />
=OffSite Meetings=<br />
<br />
We will hold some Math Circle meetings at local high schools on early release days. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<br />
<center><br />
<br />
{ style="color:black; fontsize:120%" border="1" cellpadding="14" cellspacing="0"<br />
<br />
! colspan="5" style="background: #e8b2b2;" align="center"  Fall 2017<br />
<br />
<br />
! Date !! Time !! Location !! Speaker !! Topic <br />
<br />
 October 29th  2:45pm East High School  Madison, WI  TBD  TBD <br />
<br />
 December 3rd  2:45pm East High School  Madison, WI  TBD  TBD<br />
<br />
}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 20132014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_20162017 2016  2017 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_20162017 2016  2017 Abstracts]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_20152016 2015  2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_20152016 2015  2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_20152016 2015  2015 Abstracts]<br />
<br />
[[Archived Math Circle Material]]<br />
<br />
==Link for presenters (in progress)==<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations Advice For Math Circle Presenters]<br />
<br />
[http://www.mathcircles.org/content/lessonplans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circlebox "Circle in a Box"]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16177Graduate Algebraic Geometry Seminar20181009T18:44:54Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Linear Resolutions of Edge Ideals]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 An Elementary Introduction to Geometric Langlands]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 Gonality of Curves and More]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 A Gentle introduction to Grothendieck's Galois theory]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov/David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner/Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Linear Resolutions of Edge Ideals<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Qiao He'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Elementary Introduction to Geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Wanlin Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Gonality of Curves and More<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Ewan Dalby'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A Gentle introduction to Grothendiecks Galois theory<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16152Graduate Algebraic Geometry Seminar20181005T14:50:36Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Linear Resolutions of Edge Ideals]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 An Elementary Introduction to Geometric Langlands]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 Gonality of Curves and More]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 A Gentle introduction to Grothendieck's Galois theory]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov/David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner/Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Linear Resolutions of Edge Ideals<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Qiao He'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Elementary Introduction to Geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Wanlin Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Gonality of Curves and More<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Ewan Dalby'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: A Gentle introduction to Grothendiecks Galois theory<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16084Graduate Algebraic Geometry Seminar20180928T21:11:28Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Linear Resolutions of Edge Ideals]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 An Elementary Introduction to Geometric Langlands]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 Gonality of Curves and More]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov/David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner/Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Linear Resolutions of Edge Ideals<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Qiao He'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Elementary Introduction to Geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Wanlin Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Gonality of Curves and More<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16068Graduate Algebraic Geometry Seminar20180924T21:43:23Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Linear Resolutions of Edge Ideals]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 An Elementary Introduction to Geometric Langlands]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov/David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner/Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Linear Resolutions of Edge Ideals<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Qiao He'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Elementary Introduction to Geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16067Graduate Algebraic Geometry Seminar20180924T21:42:31Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Linear Resolutions of Edge Ideals]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov/David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner/Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Caitlyn Booms'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Linear Resolutions of Edge Ideals<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Qiao He'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: An Elementary Introduction to Geometric Langlands<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
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 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=15970Graduate Algebraic Geometry Seminar20180913T00:23:32Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 TBD]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov/David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner/Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=15969Graduate Algebraic Geometry Seminar20180913T00:22:02Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:'''Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
'''Soon we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" Caitlyn Booms<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 TBD]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" Qiao He<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" Wanlin Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" Ewan Dalby<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" Johnnie Han<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov/David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" David Wagner/Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" A turkey/Smallpox<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" Asvin Gothandaraman<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" Sun Woo Park<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=15950Graduate Algebraic Geometry Seminar20180910T20:00:47Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:'''Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
'''Soon we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 Hodge Theory: One hour closer to understanding what it's about]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 TBD]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Hodge Theory: One hour closer to understanding what it's about<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
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<br />
== October 3 ==<br />
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== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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== October 17 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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== October 24 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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<br />
== October 31 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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== November 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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== November 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=15888Graduate Algebraic Geometry Seminar20180906T16:52:47Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B321 '''Pending''' (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
'''Soon we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" September 12<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 TBD]]<br />
<br />
 bgcolor="#E0E0E0" September 19<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 12 TBD]]<br />
<br />
 bgcolor="#E0E0E0" September 26<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#September 26 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 3<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 3 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 10<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 10 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 17<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 17 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 24<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 24 TBD]]<br />
<br />
 bgcolor="#E0E0E0" October 31<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#October 31 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 7<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 7 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 14<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 21<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 21 TBD]]<br />
<br />
 bgcolor="#E0E0E0" November 28<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#November 30 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 5<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 5 TBD]]<br />
<br />
 bgcolor="#E0E0E0" December 12<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#December 12 TBD]]<br />
}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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== September 19 ==<br />
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{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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== September 26 ==<br />
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== October 3 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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<br />
== October 10 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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<br />
== October 17 ==<br />
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{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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<br />
== October 24 ==<br />
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{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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<br />
== October 31 ==<br />
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{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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<br />
== November 14 ==<br />
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{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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<br />
== November 21 ==<br />
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{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
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<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== November 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 5 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=15887Graduate Algebraic Geometry Seminar20180906T16:41:27Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:00pm<br />
<br />
'''Where:'''Van Vleck B321 '''Pending''' (Fall 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 14<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 14 Fun with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 21<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 21 <math>\mathcal F</math>un with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 28<br />
 bgcolor="#C6D46E" Dima Arinkin<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 28 ODEs: algebraic vs analytic vs formal]]<br />
<br />
 bgcolor="#E0E0E0" March 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 7 Topology of Affine Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 14 Derived Quot Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 21<br />
 bgcolor="#C6D46E" Mao Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 21 D modules in prime characteristic]]<br />
<br />
 bgcolor="#E0E0E0" March 28<br />
 bgcolor="#C6D46E" Spring break<br />
 bgcolor="#BCE2FE" Whoo!<br />
<br />
 bgcolor="#E0E0E0" April 4<br />
 bgcolor="#C6D46E" Rachel Davis<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 4 Introduction to Grothendieck's dessins d'enfants]]<br />
<br />
 bgcolor="#E0E0E0" April 11<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 11 Néron models of elliptic curves]]<br />
<br />
 bgcolor="#E0E0E0" April 18<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 18 Modular forms over arbitrary rings]]<br />
<br />
 bgcolor="#E0E0E0" April 25<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 25 The Theory of Heights and the Height of Theories]]<br />
<br />
 bgcolor="#E0E0E0" May 2<br />
 bgcolor="#C6D46E" No talk today<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#May 2 Keith Rush is giving a talk at the same time]]<br />
}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Fun with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
My goal is to next week talk about Gerard Laumon's preprint ''Transformation de Fourier généralisée'', which will encapsulate all the Fourier transforms I can name (which for me includes the Fourier transform for Dmodules on affine space, the Mellin transform, the FourierMukai transform for abelian varieties and the rare John Mahoney transform between modules on the punctured line and vector spaces with a Zaction) into one crazy package.<br />
<br />
In order to achieve this altered mental state, we will have to rethink all our preconceptions, and rediscover algebraic groups, make sense of Cartier duality for them, define formal groups along the way, and see how duality of Abelian varieties relates to Cartier duality. If you come to the talk in an already in this altered mental state, then hopefully I'll do some examples that you've been too lazy to work out for yourself.<br />
<br />
} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''<math>\mathcal F</math>un with commutative groups'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: <math>\mathcal F</math>un with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will talk about how last week's Cartier duality relates to duality for abelian varieties. Then we will see how this allows us to take certain complexes of groups which are self dual, going back to altered mental states which are now derived.<br />
<br />
If we're going to Fourier transform something, it should be a sheaf, but what is even a sheaf on a complex of groups? Once we see what it should be, I will handwave what the Fourier transform is and give a bunch of concrete examples.<br />
<br />
} <br />
</center><br />
<br />
== February 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Dima Arinkin'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: ODEs: algebraic vs analytic vs formal<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Linear ordinary differential equations (or, as they are known geometrically, bundles with connections on Riemann surfaces) can be studied from many directions. In algebraic geometry, the goal is ''to classify'' equations rather than ''to solve'' them. The classification can be<br />
done in different settings: algebraic, analytic, or formal; each setting has its advantages and disadvantages. However, for one of the most<br />
important class of equations (equations with regular singularities aka Fuchsian equations) the three approaches agree, leading to a rich <br />
and beautiful picture. <br />
<br />
In my talk, I will sketch the algebraic theory of differential equations, focusing on equations with regular singularities. (I do not expect to have time<br />
for irregular singularities.) The talk is related to my topics course on Dmodules, but it does not rely on the topics course.<br />
} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Topology of Affine Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will explain in what sense flat morphisms of (affine) schemes are the correct analogue of open maps of topological spaces, and then use that to explain how surjectivity in the sense of Zariski spectra corresponds to surjectivity of functors of points.<br />
<br />
} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Derived Quot Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The titular paper of CiocanFontanine & Kapranov constructs a "derived" version of Grothendieck's Quot scheme, whose degree zero truncation is the ordinary Quot scheme, and whose tangent space at each kpoint consists higher Ext's. In this talk, we will talk about what is meant by "derived" in modern AG and why you might want a derived Quot scheme. In the remaining time, we will give a (hopefully transparent) description of how CF&K construct RQuot.<br />
<br />
} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Mao Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Dmodules in prime characteristic<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The usual theory of Dmodules concerns itself with sheaves and varieties over complex numbers. In this talk I'm going to consider its characteristic p analogue. The new feature is that the ring of differential operators has a large center. By using this extra information we can give a more precise description about the ring of differential operators, namely it has a canonical structure of an Azumaya algebra over the twisted cotangent bundle. This has lots of applications in algebraic geometry and representation theory. <br />
<br />
} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Rachel Davis'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Introduction to Grothendieck's dessins d'enfants<br />
<br />
 bgcolor="#BCD2EE"  <br />
In 1978 Bely&#301; first announced the following theorem: every algebraic curve defined over a fixed algebraic closure of the rationals can be represented as a covering of the projective line ramified over at most three points. Deligne then studied the fundamental group of the projective line minus three points. Grothendieck introduced combinatorial structures called dessins d'enfants. One consequence of Bely&#301;'s theorem is that the Galois action on the fundamental group of the projective line minus three points is faithful. <br />
} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Néron models of elliptic curves<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will attempt to do algebraic geometry over the integers. Doing this for elliptic curves will lead us to the idea of Néron models, and we will see how to get our hands on these guys explicitly.<br />
<br />
} <br />
</center><br />
<br />
== April 18 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Modular forms over arbitrary rings<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
One way to understand moduli spaces of elliptic curves and related moduli problems better, is to study modular forms. With this in mind, I will define modular forms over arbitrary rings in the sense of Katz. I will also talk about padic modular forms in the sense of Serre and hopefully motivate the modern treatment of such modular forms.<br />
<br />
} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: The Theory of Heights and the Height of Theories<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will talk about some of the different notions of height in arithmetic geometry, starting from the most naive, ending at some betterer ones.<br />
<br />
} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=15886Graduate Algebraic Geometry Seminar20180906T16:40:26Z<p>Moises: Moises moved page Graduate Algebraic Geometry Seminar to Graduate Algebraic Geometry Seminar Spring 2018: New semester!</p>
<hr />
<div>#REDIRECT [[Graduate Algebraic Geometry Seminar Spring 2018]]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=15885Graduate Algebraic Geometry Seminar Spring 201820180906T16:40:25Z<p>Moises: Moises moved page Graduate Algebraic Geometry Seminar to Graduate Algebraic Geometry Seminar Spring 2018: New semester!</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 14<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 14 Fun with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 21<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 21 <math>\mathcal F</math>un with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 28<br />
 bgcolor="#C6D46E" Dima Arinkin<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 28 ODEs: algebraic vs analytic vs formal]]<br />
<br />
 bgcolor="#E0E0E0" March 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 7 Topology of Affine Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 14 Derived Quot Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 21<br />
 bgcolor="#C6D46E" Mao Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 21 D modules in prime characteristic]]<br />
<br />
 bgcolor="#E0E0E0" March 28<br />
 bgcolor="#C6D46E" Spring break<br />
 bgcolor="#BCE2FE" Whoo!<br />
<br />
 bgcolor="#E0E0E0" April 4<br />
 bgcolor="#C6D46E" Rachel Davis<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 4 Introduction to Grothendieck's dessins d'enfants]]<br />
<br />
 bgcolor="#E0E0E0" April 11<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 11 Néron models of elliptic curves]]<br />
<br />
 bgcolor="#E0E0E0" April 18<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 18 Modular forms over arbitrary rings]]<br />
<br />
 bgcolor="#E0E0E0" April 25<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 25 The Theory of Heights and the Height of Theories]]<br />
<br />
 bgcolor="#E0E0E0" May 2<br />
 bgcolor="#C6D46E" No talk today<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#May 2 Keith Rush is giving a talk at the same time]]<br />
}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Fun with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
My goal is to next week talk about Gerard Laumon's preprint ''Transformation de Fourier généralisée'', which will encapsulate all the Fourier transforms I can name (which for me includes the Fourier transform for Dmodules on affine space, the Mellin transform, the FourierMukai transform for abelian varieties and the rare John Mahoney transform between modules on the punctured line and vector spaces with a Zaction) into one crazy package.<br />
<br />
In order to achieve this altered mental state, we will have to rethink all our preconceptions, and rediscover algebraic groups, make sense of Cartier duality for them, define formal groups along the way, and see how duality of Abelian varieties relates to Cartier duality. If you come to the talk in an already in this altered mental state, then hopefully I'll do some examples that you've been too lazy to work out for yourself.<br />
<br />
} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''<math>\mathcal F</math>un with commutative groups'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: <math>\mathcal F</math>un with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will talk about how last week's Cartier duality relates to duality for abelian varieties. Then we will see how this allows us to take certain complexes of groups which are self dual, going back to altered mental states which are now derived.<br />
<br />
If we're going to Fourier transform something, it should be a sheaf, but what is even a sheaf on a complex of groups? Once we see what it should be, I will handwave what the Fourier transform is and give a bunch of concrete examples.<br />
<br />
} <br />
</center><br />
<br />
== February 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Dima Arinkin'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: ODEs: algebraic vs analytic vs formal<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Linear ordinary differential equations (or, as they are known geometrically, bundles with connections on Riemann surfaces) can be studied from many directions. In algebraic geometry, the goal is ''to classify'' equations rather than ''to solve'' them. The classification can be<br />
done in different settings: algebraic, analytic, or formal; each setting has its advantages and disadvantages. However, for one of the most<br />
important class of equations (equations with regular singularities aka Fuchsian equations) the three approaches agree, leading to a rich <br />
and beautiful picture. <br />
<br />
In my talk, I will sketch the algebraic theory of differential equations, focusing on equations with regular singularities. (I do not expect to have time<br />
for irregular singularities.) The talk is related to my topics course on Dmodules, but it does not rely on the topics course.<br />
} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Topology of Affine Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will explain in what sense flat morphisms of (affine) schemes are the correct analogue of open maps of topological spaces, and then use that to explain how surjectivity in the sense of Zariski spectra corresponds to surjectivity of functors of points.<br />
<br />
} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Derived Quot Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The titular paper of CiocanFontanine & Kapranov constructs a "derived" version of Grothendieck's Quot scheme, whose degree zero truncation is the ordinary Quot scheme, and whose tangent space at each kpoint consists higher Ext's. In this talk, we will talk about what is meant by "derived" in modern AG and why you might want a derived Quot scheme. In the remaining time, we will give a (hopefully transparent) description of how CF&K construct RQuot.<br />
<br />
} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Mao Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Dmodules in prime characteristic<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The usual theory of Dmodules concerns itself with sheaves and varieties over complex numbers. In this talk I'm going to consider its characteristic p analogue. The new feature is that the ring of differential operators has a large center. By using this extra information we can give a more precise description about the ring of differential operators, namely it has a canonical structure of an Azumaya algebra over the twisted cotangent bundle. This has lots of applications in algebraic geometry and representation theory. <br />
<br />
} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Rachel Davis'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Introduction to Grothendieck's dessins d'enfants<br />
<br />
 bgcolor="#BCD2EE"  <br />
In 1978 Bely&#301; first announced the following theorem: every algebraic curve defined over a fixed algebraic closure of the rationals can be represented as a covering of the projective line ramified over at most three points. Deligne then studied the fundamental group of the projective line minus three points. Grothendieck introduced combinatorial structures called dessins d'enfants. One consequence of Bely&#301;'s theorem is that the Galois action on the fundamental group of the projective line minus three points is faithful. <br />
} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Néron models of elliptic curves<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will attempt to do algebraic geometry over the integers. Doing this for elliptic curves will lead us to the idea of Néron models, and we will see how to get our hands on these guys explicitly.<br />
<br />
} <br />
</center><br />
<br />
== April 18 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Modular forms over arbitrary rings<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
One way to understand moduli spaces of elliptic curves and related moduli problems better, is to study modular forms. With this in mind, I will define modular forms over arbitrary rings in the sense of Katz. I will also talk about padic modular forms in the sense of Serre and hopefully motivate the modern treatment of such modular forms.<br />
<br />
} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: The Theory of Heights and the Height of Theories<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will talk about some of the different notions of height in arithmetic geometry, starting from the most naive, ending at some betterer ones.<br />
<br />
} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=15460Graduate Algebraic Geometry Seminar Spring 201820180424T21:10:07Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 14<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 14 Fun with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 21<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 21 <math>\mathcal F</math>un with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 28<br />
 bgcolor="#C6D46E" Dima Arinkin<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 28 ODEs: algebraic vs analytic vs formal]]<br />
<br />
 bgcolor="#E0E0E0" March 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 7 Topology of Affine Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 14 Derived Quot Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 21<br />
 bgcolor="#C6D46E" Mao Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 21 D modules in prime characteristic]]<br />
<br />
 bgcolor="#E0E0E0" March 28<br />
 bgcolor="#C6D46E" Spring break<br />
 bgcolor="#BCE2FE" Whoo!<br />
<br />
 bgcolor="#E0E0E0" April 4<br />
 bgcolor="#C6D46E" Rachel Davis<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 4 Introduction to Grothendieck's dessins d'enfants]]<br />
<br />
 bgcolor="#E0E0E0" April 11<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 11 Néron models of elliptic curves]]<br />
<br />
 bgcolor="#E0E0E0" April 18<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 18 Modular forms over arbitrary rings]]<br />
<br />
 bgcolor="#E0E0E0" April 25<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 25 The Theory of Heights and the Height of Theories]]<br />
<br />
 bgcolor="#E0E0E0" May 2<br />
 bgcolor="#C6D46E" No talk today<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#May 2 Keith Rush is giving a talk at the same time]]<br />
}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Fun with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
My goal is to next week talk about Gerard Laumon's preprint ''Transformation de Fourier généralisée'', which will encapsulate all the Fourier transforms I can name (which for me includes the Fourier transform for Dmodules on affine space, the Mellin transform, the FourierMukai transform for abelian varieties and the rare John Mahoney transform between modules on the punctured line and vector spaces with a Zaction) into one crazy package.<br />
<br />
In order to achieve this altered mental state, we will have to rethink all our preconceptions, and rediscover algebraic groups, make sense of Cartier duality for them, define formal groups along the way, and see how duality of Abelian varieties relates to Cartier duality. If you come to the talk in an already in this altered mental state, then hopefully I'll do some examples that you've been too lazy to work out for yourself.<br />
<br />
} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''<math>\mathcal F</math>un with commutative groups'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: <math>\mathcal F</math>un with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will talk about how last week's Cartier duality relates to duality for abelian varieties. Then we will see how this allows us to take certain complexes of groups which are self dual, going back to altered mental states which are now derived.<br />
<br />
If we're going to Fourier transform something, it should be a sheaf, but what is even a sheaf on a complex of groups? Once we see what it should be, I will handwave what the Fourier transform is and give a bunch of concrete examples.<br />
<br />
} <br />
</center><br />
<br />
== February 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Dima Arinkin'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: ODEs: algebraic vs analytic vs formal<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Linear ordinary differential equations (or, as they are known geometrically, bundles with connections on Riemann surfaces) can be studied from many directions. In algebraic geometry, the goal is ''to classify'' equations rather than ''to solve'' them. The classification can be<br />
done in different settings: algebraic, analytic, or formal; each setting has its advantages and disadvantages. However, for one of the most<br />
important class of equations (equations with regular singularities aka Fuchsian equations) the three approaches agree, leading to a rich <br />
and beautiful picture. <br />
<br />
In my talk, I will sketch the algebraic theory of differential equations, focusing on equations with regular singularities. (I do not expect to have time<br />
for irregular singularities.) The talk is related to my topics course on Dmodules, but it does not rely on the topics course.<br />
} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Topology of Affine Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will explain in what sense flat morphisms of (affine) schemes are the correct analogue of open maps of topological spaces, and then use that to explain how surjectivity in the sense of Zariski spectra corresponds to surjectivity of functors of points.<br />
<br />
} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Derived Quot Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The titular paper of CiocanFontanine & Kapranov constructs a "derived" version of Grothendieck's Quot scheme, whose degree zero truncation is the ordinary Quot scheme, and whose tangent space at each kpoint consists higher Ext's. In this talk, we will talk about what is meant by "derived" in modern AG and why you might want a derived Quot scheme. In the remaining time, we will give a (hopefully transparent) description of how CF&K construct RQuot.<br />
<br />
} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Mao Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Dmodules in prime characteristic<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The usual theory of Dmodules concerns itself with sheaves and varieties over complex numbers. In this talk I'm going to consider its characteristic p analogue. The new feature is that the ring of differential operators has a large center. By using this extra information we can give a more precise description about the ring of differential operators, namely it has a canonical structure of an Azumaya algebra over the twisted cotangent bundle. This has lots of applications in algebraic geometry and representation theory. <br />
<br />
} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Rachel Davis'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Introduction to Grothendieck's dessins d'enfants<br />
<br />
 bgcolor="#BCD2EE"  <br />
In 1978 Bely&#301; first announced the following theorem: every algebraic curve defined over a fixed algebraic closure of the rationals can be represented as a covering of the projective line ramified over at most three points. Deligne then studied the fundamental group of the projective line minus three points. Grothendieck introduced combinatorial structures called dessins d'enfants. One consequence of Bely&#301;'s theorem is that the Galois action on the fundamental group of the projective line minus three points is faithful. <br />
} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Néron models of elliptic curves<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will attempt to do algebraic geometry over the integers. Doing this for elliptic curves will lead us to the idea of Néron models, and we will see how to get our hands on these guys explicitly.<br />
<br />
} <br />
</center><br />
<br />
== April 18 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Modular forms over arbitrary rings<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
One way to understand moduli spaces of elliptic curves and related moduli problems better, is to study modular forms. With this in mind, I will define modular forms over arbitrary rings in the sense of Katz. I will also talk about padic modular forms in the sense of Serre and hopefully motivate the modern treatment of such modular forms.<br />
<br />
} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Solly Parenti'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: The Theory of Heights and the Height of Theories<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will talk about some of the different notions of height in arithmetic geometry, starting from the most naive, ending at some betterer ones.<br />
<br />
} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=15430Graduate Algebraic Geometry Seminar Spring 201820180417T20:53:18Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 14<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 14 Fun with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 21<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 21 <math>\mathcal F</math>un with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 28<br />
 bgcolor="#C6D46E" Dima Arinkin<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 28 ODEs: algebraic vs analytic vs formal]]<br />
<br />
 bgcolor="#E0E0E0" March 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 7 Topology of Affine Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 14 Derived Quot Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 21<br />
 bgcolor="#C6D46E" Mao Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 21 D modules in prime characteristic]]<br />
<br />
 bgcolor="#E0E0E0" March 28<br />
 bgcolor="#C6D46E" Spring break<br />
 bgcolor="#BCE2FE" Whoo!<br />
<br />
 bgcolor="#E0E0E0" April 4<br />
 bgcolor="#C6D46E" Rachel Davis<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 4 Introduction to Grothendieck's dessins d'enfants]]<br />
<br />
 bgcolor="#E0E0E0" April 11<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 11 Néron models of elliptic curves]]<br />
<br />
 bgcolor="#E0E0E0" April 18<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 18 Modular forms over arbitrary rings]]<br />
<br />
 bgcolor="#E0E0E0" April 25<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 25 TBD]]<br />
<br />
 bgcolor="#E0E0E0" May 2<br />
 bgcolor="#C6D46E" Jordan Ellenberg<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#May 2 Sabotage]]<br />
}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Fun with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
My goal is to next week talk about Gerard Laumon's preprint ''Transformation de Fourier généralisée'', which will encapsulate all the Fourier transforms I can name (which for me includes the Fourier transform for Dmodules on affine space, the Mellin transform, the FourierMukai transform for abelian varieties and the rare John Mahoney transform between modules on the punctured line and vector spaces with a Zaction) into one crazy package.<br />
<br />
In order to achieve this altered mental state, we will have to rethink all our preconceptions, and rediscover algebraic groups, make sense of Cartier duality for them, define formal groups along the way, and see how duality of Abelian varieties relates to Cartier duality. If you come to the talk in an already in this altered mental state, then hopefully I'll do some examples that you've been too lazy to work out for yourself.<br />
<br />
} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''<math>\mathcal F</math>un with commutative groups'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: <math>\mathcal F</math>un with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will talk about how last week's Cartier duality relates to duality for abelian varieties. Then we will see how this allows us to take certain complexes of groups which are self dual, going back to altered mental states which are now derived.<br />
<br />
If we're going to Fourier transform something, it should be a sheaf, but what is even a sheaf on a complex of groups? Once we see what it should be, I will handwave what the Fourier transform is and give a bunch of concrete examples.<br />
<br />
} <br />
</center><br />
<br />
== February 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Dima Arinkin'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: ODEs: algebraic vs analytic vs formal<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Linear ordinary differential equations (or, as they are known geometrically, bundles with connections on Riemann surfaces) can be studied from many directions. In algebraic geometry, the goal is ''to classify'' equations rather than ''to solve'' them. The classification can be<br />
done in different settings: algebraic, analytic, or formal; each setting has its advantages and disadvantages. However, for one of the most<br />
important class of equations (equations with regular singularities aka Fuchsian equations) the three approaches agree, leading to a rich <br />
and beautiful picture. <br />
<br />
In my talk, I will sketch the algebraic theory of differential equations, focusing on equations with regular singularities. (I do not expect to have time<br />
for irregular singularities.) The talk is related to my topics course on Dmodules, but it does not rely on the topics course.<br />
} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Topology of Affine Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will explain in what sense flat morphisms of (affine) schemes are the correct analogue of open maps of topological spaces, and then use that to explain how surjectivity in the sense of Zariski spectra corresponds to surjectivity of functors of points.<br />
<br />
} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Derived Quot Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The titular paper of CiocanFontanine & Kapranov constructs a "derived" version of Grothendieck's Quot scheme, whose degree zero truncation is the ordinary Quot scheme, and whose tangent space at each kpoint consists higher Ext's. In this talk, we will talk about what is meant by "derived" in modern AG and why you might want a derived Quot scheme. In the remaining time, we will give a (hopefully transparent) description of how CF&K construct RQuot.<br />
<br />
} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Mao Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Dmodules in prime characteristic<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The usual theory of Dmodules concerns itself with sheaves and varieties over complex numbers. In this talk I'm going to consider its characteristic p analogue. The new feature is that the ring of differential operators has a large center. By using this extra information we can give a more precise description about the ring of differential operators, namely it has a canonical structure of an Azumaya algebra over the twisted cotangent bundle. This has lots of applications in algebraic geometry and representation theory. <br />
<br />
} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Rachel Davis'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Introduction to Grothendieck's dessins d'enfants<br />
<br />
 bgcolor="#BCD2EE"  <br />
In 1978 Bely&#301; first announced the following theorem: every algebraic curve defined over a fixed algebraic closure of the rationals can be represented as a covering of the projective line ramified over at most three points. Deligne then studied the fundamental group of the projective line minus three points. Grothendieck introduced combinatorial structures called dessins d'enfants. One consequence of Bely&#301;'s theorem is that the Galois action on the fundamental group of the projective line minus three points is faithful. <br />
} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Néron models of elliptic curves<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will attempt to do algebraic geometry over the integers. Doing this for elliptic curves will lead us to the idea of Néron models, and we will see how to get our hands on these guys explicitly.<br />
<br />
} <br />
</center><br />
<br />
== April 18 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Modular forms over arbitrary rings<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
One way to understand moduli spaces of elliptic curves and related moduli problems better, is to study modular forms. With this in mind, I will define modular forms over arbitrary rings in the sense of Katz. I will also talk about padic modular forms in the sense of Serre and hopefully motivate the modern treatment of such modular forms.<br />
<br />
} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== May 2 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Keith Rush'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Sabotage<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
A very special speaker will speak in a very special setting, invited by someone else. This will result in GAGS crumbling into its ashes possibly to never be reborn from them.<br />
<br />
} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=15429Graduate Algebraic Geometry Seminar Spring 201820180417T20:51:04Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 14<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 14 Fun with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 21<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 21 <math>\mathcal F</math>un with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 28<br />
 bgcolor="#C6D46E" Dima Arinkin<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 28 ODEs: algebraic vs analytic vs formal]]<br />
<br />
 bgcolor="#E0E0E0" March 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 7 Topology of Affine Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 14 Derived Quot Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 21<br />
 bgcolor="#C6D46E" Mao Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 21 D modules in prime characteristic]]<br />
<br />
 bgcolor="#E0E0E0" March 28<br />
 bgcolor="#C6D46E" Spring break<br />
 bgcolor="#BCE2FE" Whoo!<br />
<br />
 bgcolor="#E0E0E0" April 4<br />
 bgcolor="#C6D46E" Rachel Davis<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 4 Introduction to Grothendieck's dessins d'enfants]]<br />
<br />
 bgcolor="#E0E0E0" April 11<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 11 TBD]]<br />
<br />
 bgcolor="#E0E0E0" April 18<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 18 TBD]]<br />
<br />
 bgcolor="#E0E0E0" April 25<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 25 TBD]]<br />
<br />
 bgcolor="#E0E0E0" May 2<br />
 bgcolor="#C6D46E" Jordan Ellenberg<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#May 2 Sabotage]]<br />
}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Fun with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
My goal is to next week talk about Gerard Laumon's preprint ''Transformation de Fourier généralisée'', which will encapsulate all the Fourier transforms I can name (which for me includes the Fourier transform for Dmodules on affine space, the Mellin transform, the FourierMukai transform for abelian varieties and the rare John Mahoney transform between modules on the punctured line and vector spaces with a Zaction) into one crazy package.<br />
<br />
In order to achieve this altered mental state, we will have to rethink all our preconceptions, and rediscover algebraic groups, make sense of Cartier duality for them, define formal groups along the way, and see how duality of Abelian varieties relates to Cartier duality. If you come to the talk in an already in this altered mental state, then hopefully I'll do some examples that you've been too lazy to work out for yourself.<br />
<br />
} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''<math>\mathcal F</math>un with commutative groups'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: <math>\mathcal F</math>un with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will talk about how last week's Cartier duality relates to duality for abelian varieties. Then we will see how this allows us to take certain complexes of groups which are self dual, going back to altered mental states which are now derived.<br />
<br />
If we're going to Fourier transform something, it should be a sheaf, but what is even a sheaf on a complex of groups? Once we see what it should be, I will handwave what the Fourier transform is and give a bunch of concrete examples.<br />
<br />
} <br />
</center><br />
<br />
== February 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Dima Arinkin'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: ODEs: algebraic vs analytic vs formal<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Linear ordinary differential equations (or, as they are known geometrically, bundles with connections on Riemann surfaces) can be studied from many directions. In algebraic geometry, the goal is ''to classify'' equations rather than ''to solve'' them. The classification can be<br />
done in different settings: algebraic, analytic, or formal; each setting has its advantages and disadvantages. However, for one of the most<br />
important class of equations (equations with regular singularities aka Fuchsian equations) the three approaches agree, leading to a rich <br />
and beautiful picture. <br />
<br />
In my talk, I will sketch the algebraic theory of differential equations, focusing on equations with regular singularities. (I do not expect to have time<br />
for irregular singularities.) The talk is related to my topics course on Dmodules, but it does not rely on the topics course.<br />
} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Topology of Affine Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will explain in what sense flat morphisms of (affine) schemes are the correct analogue of open maps of topological spaces, and then use that to explain how surjectivity in the sense of Zariski spectra corresponds to surjectivity of functors of points.<br />
<br />
} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Derived Quot Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The titular paper of CiocanFontanine & Kapranov constructs a "derived" version of Grothendieck's Quot scheme, whose degree zero truncation is the ordinary Quot scheme, and whose tangent space at each kpoint consists higher Ext's. In this talk, we will talk about what is meant by "derived" in modern AG and why you might want a derived Quot scheme. In the remaining time, we will give a (hopefully transparent) description of how CF&K construct RQuot.<br />
<br />
} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Mao Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Dmodules in prime characteristic<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The usual theory of Dmodules concerns itself with sheaves and varieties over complex numbers. In this talk I'm going to consider its characteristic p analogue. The new feature is that the ring of differential operators has a large center. By using this extra information we can give a more precise description about the ring of differential operators, namely it has a canonical structure of an Azumaya algebra over the twisted cotangent bundle. This has lots of applications in algebraic geometry and representation theory. <br />
<br />
} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Rachel Davis'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Introduction to Grothendieck's dessins d'enfants<br />
<br />
 bgcolor="#BCD2EE"  <br />
In 1978 Bely&#301; first announced the following theorem: every algebraic curve defined over a fixed algebraic closure of the rationals can be represented as a covering of the projective line ramified over at most three points. Deligne then studied the fundamental group of the projective line minus three points. Grothendieck introduced combinatorial structures called dessins d'enfants. One consequence of Bely&#301;'s theorem is that the Galois action on the fundamental group of the projective line minus three points is faithful. <br />
} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Brandon Boggess'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Néron models of elliptic curves<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
We will attempt to do algebraic geometry over the integers. Doing this for elliptic curves will lead us to the idea of Néron models, and we will see how to get our hands on these guys explicitly.<br />
<br />
} <br />
</center><br />
<br />
== April 18 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Soumya Sankar'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Modular forms over arbitrary rings<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
One way to understand moduli spaces of elliptic curves and related moduli problems better, is to study modular forms. With this in mind, I will define modular forms over arbitrary rings in the sense of Katz. I will also talk about padic modular forms in the sense of Serre and hopefully motivate the modern treatment of such modular forms.<br />
<br />
} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== May 2 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Keith Rush'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Sabotage<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
A very special speaker will speak in a very special setting, invited by someone else. This will result in GAGS crumbling into its ashes possibly to never be reborn from them.<br />
<br />
} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Abelian_Varieties_2018&diff=15254Abelian Varieties 201820180314T20:30:17Z<p>Moises: </p>
<hr />
<div>== Overview ==<br />
This reading seminar will cover Kempf's "Complex Abelian Varieties and Theta Functions" book. Talks will be Mondays, 4:004:50 in Room B139.<br />
<br />
We can try to cover Chapters 17 and Chapter 11 and maybe some topics from the other chapters of Birkenhake and Lange's "Complex Abelian Varieties" as time permits.<br />
<br />
== Talk Schedule ==<br />
The following schedule might be adjusted as we go, depending on whether it seems too fast or not.<br />
<br />
Here is the [[https://www.math.wisc.edu/wiki/images/TOC.pdf Table of Contents]] of Kempf's book.<br />
<br />
{ cellpadding="8"<br />
!align="left"  date<br />
!align="left"  speaker<br />
!align="left"  sections<br />
<br />
<br />
February 7<br />
Rachel Davis<br />
1.11.3<br />
<br />
February 12<br />
Soumya Sankar<br />
1.41.5<br />
<br />
February 19<br />
Michael Brown<br />
2.12.2<br />
<br />
February 26<br />
Solly Parenti<br />
2.32.4<br />
<br />
March 5<br />
Vladimir Sotirov<br />
3.13.3<br />
<br />
March 12<br />
Moisés Herradón Cueto<br />
3.43.6 [https://www.math.wisc.edu/wiki/images/AbVars_Secs3.43.6.pdf My notes]<br />
<br />
March 19<br />
Brandon Boggess<br />
4<br />
<br />
March 26<br />
No meeting<br />
Spring Break<br />
<br />
April 2<br />
Mao Li<br />
5.15.3<br />
<br />
April 9<br />
Hang Huang<br />
5.35.5<br />
<br />
April 16<br />
TBD<br />
6<br />
<br />
April 23<br />
Daniel Erman<br />
7<br />
<br />
April 30<br />
Wanlin Li<br />
11<br />
<br />
May 7<br />
TBD<br />
???<br />
<br />
}</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Abelian_Varieties_2018&diff=15253Abelian Varieties 201820180314T20:29:49Z<p>Moises: </p>
<hr />
<div>== Overview ==<br />
This reading seminar will cover Kempf's "Complex Abelian Varieties and Theta Functions" book. Talks will be Mondays, 4:004:50 in Room B139.<br />
<br />
We can try to cover Chapters 17 and Chapter 11 and maybe some topics from the other chapters of Birkenhake and Lange's "Complex Abelian Varieties" as time permits.<br />
<br />
== Talk Schedule ==<br />
The following schedule might be adjusted as we go, depending on whether it seems too fast or not.<br />
<br />
Here is the [[https://www.math.wisc.edu/wiki/images/TOC.pdf Table of Contents]] of Kempf's book.<br />
<br />
{ cellpadding="8"<br />
!align="left"  date<br />
!align="left"  speaker<br />
!align="left"  sections<br />
<br />
<br />
February 7<br />
Rachel Davis<br />
1.11.3<br />
<br />
February 12<br />
Soumya Sankar<br />
1.41.5<br />
<br />
February 19<br />
Michael Brown<br />
2.12.2<br />
<br />
February 26<br />
Solly Parenti<br />
2.32.4<br />
<br />
March 5<br />
Vladimir Sotirov<br />
3.13.3<br />
<br />
March 12<br />
Moisés Herradón Cueto<br />
3.43.6 [[https://www.math.wisc.edu/wiki/images/AbVars_Secs3.43.6.pdf My notes]]<br />
<br />
March 19<br />
Brandon Boggess<br />
4<br />
<br />
March 26<br />
No meeting<br />
Spring Break<br />
<br />
April 2<br />
Mao Li<br />
5.15.3<br />
<br />
April 9<br />
Hang Huang<br />
5.35.5<br />
<br />
April 16<br />
TBD<br />
6<br />
<br />
April 23<br />
Daniel Erman<br />
7<br />
<br />
April 30<br />
Wanlin Li<br />
11<br />
<br />
May 7<br />
TBD<br />
???<br />
<br />
}</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=File:AbVars_Secs3.43.6.pdf&diff=15252File:AbVars Secs3.43.6.pdf20180314T20:29:13Z<p>Moises: </p>
<hr />
<div></div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=15242Graduate Algebraic Geometry Seminar Spring 201820180313T04:38:55Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 14<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 14 Fun with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 21<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 21 <math>\mathcal F</math>un with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 28<br />
 bgcolor="#C6D46E" Dima Arinkin<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 28 ODEs: algebraic vs analytic vs formal]]<br />
<br />
 bgcolor="#E0E0E0" March 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 7 Topology of Affine Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 14 Derived Quot Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 21<br />
 bgcolor="#C6D46E" Mao Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 21 D modules in prime characteristic]]<br />
<br />
 bgcolor="#E0E0E0" March 28<br />
 bgcolor="#C6D46E" Spring break<br />
 bgcolor="#BCE2FE" Whoo!<br />
<br />
 bgcolor="#E0E0E0" April 4<br />
 bgcolor="#C6D46E" Rachel Davis<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 4 TBD]]<br />
<br />
 bgcolor="#E0E0E0" April 11<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 11 TBD]]<br />
<br />
 bgcolor="#E0E0E0" April 18<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 18 TBD]]<br />
<br />
 bgcolor="#E0E0E0" April 25<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 25 TBD]]<br />
<br />
 bgcolor="#E0E0E0" May 2<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#May 2 TBD]]<br />
}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Fun with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
My goal is to next week talk about Gerard Laumon's preprint ''Transformation de Fourier généralisée'', which will encapsulate all the Fourier transforms I can name (which for me includes the Fourier transform for Dmodules on affine space, the Mellin transform, the FourierMukai transform for abelian varieties and the rare John Mahoney transform between modules on the punctured line and vector spaces with a Zaction) into one crazy package.<br />
<br />
In order to achieve this altered mental state, we will have to rethink all our preconceptions, and rediscover algebraic groups, make sense of Cartier duality for them, define formal groups along the way, and see how duality of Abelian varieties relates to Cartier duality. If you come to the talk in an already in this altered mental state, then hopefully I'll do some examples that you've been too lazy to work out for yourself.<br />
<br />
} <br />
</center><br />
<br />
== February 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''<math>\mathcal F</math>un with commutative groups'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: <math>\mathcal F</math>un with commutative groups<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will talk about how last week's Cartier duality relates to duality for abelian varieties. Then we will see how this allows us to take certain complexes of groups which are self dual, going back to altered mental states which are now derived.<br />
<br />
If we're going to Fourier transform something, it should be a sheaf, but what is even a sheaf on a complex of groups? Once we see what it should be, I will handwave what the Fourier transform is and give a bunch of concrete examples.<br />
<br />
} <br />
</center><br />
<br />
== February 28 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Dima Arinkin'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: ODEs: algebraic vs analytic vs formal<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
Linear ordinary differential equations (or, as they are known geometrically, bundles with connections on Riemann surfaces) can be studied from many directions. In algebraic geometry, the goal is ''to classify'' equations rather than ''to solve'' them. The classification can be<br />
done in different settings: algebraic, analytic, or formal; each setting has its advantages and disadvantages. However, for one of the most<br />
important class of equations (equations with regular singularities aka Fuchsian equations) the three approaches agree, leading to a rich <br />
and beautiful picture. <br />
<br />
In my talk, I will sketch the algebraic theory of differential equations, focusing on equations with regular singularities. (I do not expect to have time<br />
for irregular singularities.) The talk is related to my topics course on Dmodules, but it does not rely on the topics course.<br />
} <br />
</center><br />
<br />
== March 7 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Vladimir Sotirov'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Topology of Affine Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
I will explain in what sense flat morphisms of (affine) schemes are the correct analogue of open maps of topological spaces, and then use that to explain how surjectivity in the sense of Zariski spectra corresponds to surjectivity of functors of points.<br />
<br />
} <br />
</center><br />
<br />
== March 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''David Wagner'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Derived Quot Schemes<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
The titular paper of CiocanFontanine & Kapranov constructs a "derived" version of Grothendieck's Quot scheme, whose degree zero truncation is the ordinary Quot scheme, and whose tangent space at each kpoint consists higher Ext's. In this talk, we will talk about what is meant by "derived" in modern AG and why you might want a derived Quot scheme. In the remaining time, we will give a (hopefully transparent) description of how CF&K construct RQuot.<br />
<br />
} <br />
</center><br />
<br />
== March 21 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Mao Li'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Dmodules in prime characteristic<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== April 4 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== April 11 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== April 18 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== April 25 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
== May 2 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''TBD'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: TBD<br />
<br />
 bgcolor="#BCD2EE"  <br />
Abstract: <br />
<br />
TBD<br />
<br />
} <br />
</center><br />
<br />
<br />
== Organizers' Contact Info ==<br />
[http://www.math.wisc.edu/~juliettebruce Juliette Bruce]<br />
<br />
[http://www.math.wisc.edu/~clement Nathan Clement]<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Moiseshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2018&diff=15241Graduate Algebraic Geometry Seminar Spring 201820180313T04:38:03Z<p>Moises: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 3:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2018)<br />
[[Image:cat.jpgthumb220px  Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying indepth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.<br />
<br />
'''How:'''If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:juliette.bruce@math.wisc.edu Juliette] or [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in threedimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. ''What is the Grassmanian, you say?'' That's probably a talk we should have every year, so you should give it!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry  Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann  Roch. (Grothendieck  Riemann  Roch? Hirzebruch  Riemann  Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with Dmodules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov1719(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* Dmodules 101: basics of Dmodules, equivalence between left and right Dmodules, pullbacks, pushforwards, maybe the GaussManin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on Dmodules (the point is that then you can get a FourierMukai transform between certain Omodules and certain Dmodules, which is more or less how geometric Langlands is supposed to work)<br />
<br />
===Famous Theorems===<br />
<br />
===Interesting Papers & Books===<br />
* ''Symplectic structure of the moduli space of sheaves on an abelian or K3 surface''  Shigeru Mukai.<br />
<br />
* ''Residues and Duality''  Robin Hatshorne.<br />
** Have you heard of Serre Duality? Would you like to really understand the nuts and bolts of it and its generalizations? If so this book is for you. (You wouldn't need to read the whole book to give a talk ;).)<br />
<br />
* ''Coherent sheaves on P^n and problems in linear algebra''  A. A. Beilinson.<br />
** In this two page paper constructs the semiorthogonal decomposition of the derived category of coherent sheaves on projective space. (This topic is very important, and there are a ton of other resources for this result and the general theory of derived categories.)<br />
<br />
* ''Frobenius splitting and cohomology vanishing for Schubert varieties''  V.B. Mehta and A. Ramanathan.<br />
** In characteristic p the fact that (x+y)^p=x^p+y^p means that one has the Frobenius morphism, which sends f to f^p. In this paper the authors introduce the notion of what it means for a variety to be Frobenius split, and use this to prove certain cohomologcal vanishing results for Schubert varieties. Since then Frobenius splitting  and its related cousins (Fregularity, strong Fregularity, Fpurity, etc.) have played large roles in geometry and algebra in characteristic p. This is a good place to get a sense for what kicked all this stuff off! <br />
<br />
* ''Schubert Calculus''  S. L. Kleiman and Dan Laksov.<br />
** An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!<br />
<br />
* ''Rational Isogenies of Prime Degree''  Barry Mazur.<br />
** In this paper Mazur classifies all isogenies of rational elliptic curves of prime order. As a result of this he deduces his famous result that the torsion subgroup of an elliptic curve (over Q) is one of 15 abelian groups. This definitely stares into the land of number theory, but certainly would still be of interest to many.<br />
<br />
* ''Esquisse d’une programme''  Alexander Grothendieck.<br />
** Originating from a grant proposal in the mid 1980's this famous paper outlines a tantalizing research program, which seeks to tie numerous different areas of math (algebraic geometry, Teichmuller theory, Galois theory, etc.) together. This is where Grothendieck introduced his famous Lego game and dessin d'enfant. While just a research proposal this paper has seemingly inspired a ton of cool math, and will allow you to "blow peoples’ minds". (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Géométrie algébraique et géométrie analytique''  J.P. Serre.<br />
** A projective variety X over the complex numbers has two lives, an algebraic and an analytic, depending on which topology one wishes to work with. That is one can think about X as a complex manifold and work with holomorphic functions or as an algebraic variety and work with regular functions. Hence to any complex projective variety we have two sheaf theories and as a result two cohomology theories. In this famous paper Serre compares these two and shows they are in fact the same. (''Note: This is a super fundamental result that is used all the time; normally in the following way: Uhh... What do you mean by cohomology? Well by GAGA or something it doesn't really mater.) (The original paper is in French, but there are English translations out there.)<br />
<br />
* ''Limit linear series: Basic theory'' David Eisenbud and Joe Harris.<br />
** One of the more profitable tools  especially when studying moduli spaces  in a geometers tool box is the theory of degenerations. However, sometimes we care about more than just the variety we are degenerating and want to keep track of things like vector/line bundles. In this paper Eisenbud and Harris develop the theory of degenerating a curve together with a linear series. From this they prove a ton of cool results: M_g is of general type for g>24, BrillNoether theory, etc.<br />
<br />
* ''Picard Groups of Moduli Problems''  David Mumford.<br />
** This paper is essentially the origin of algebraic stacks.<br />
<br />
* ''The Structure of Algebraic Threefolds: An Introduction to Mori's Program''  Janos Kollar<br />
** This paper is an introduction to Mori's famous ``minimal model'' program, which is a far reaching program seeking to understand the birational geometry of higher dimensional varieties. <br />
<br />
* ''CayleyBacharach Formulas''  Qingchun Ren, Jürgen RichterGebert, Bernd Sturmfels.<br />
** A classical result we all learn in a first semester of algebraic geometry is that 5 points in the plane (in general position) determine a unique plane conic. One can similarly show that 9 (general) points in the plane determine a unique plane cubic curve. This paper tries to answer the question: ``What is equation for this cubic curve?''.<br />
<br />
* ''On Varieties of Minimal Degree (A Centennial Approach)''  David Eisenbud and Joe Harris.<br />
** Suppose X is a projective variety embedded in projective space so that X is not contained in any hyperplane. By projecting from general points one can see that the degree of X is at least codim(X)+1. This paper discusses the classification of varieties that achieve this lower degree bound i.e. varieties of minimal degree. This topic is quite classical and the paper seems to contain a nice mixture of classical and modern geometry.<br />
<br />
* ''The GromovWitten potential associated to a TCFT''  Kevin J. Costello.<br />
** This seems incredibly interesting, but fairing warning this paper has been described as ''highly technical'', which considering it uses Ainfinity algebras and the derived category of a CalabiYau seems like a reasonable description. (This paper may be covered in Caldararu's Spring 2017 topics course.)<br />
__NOTOC__<br />
<br />
== Spring 2017 ==<br />
<br />
<center><br />
{ style="color:black; fontsize:120%" border="0" cellpadding="14" cellspacing="5"<br />
<br />
 bgcolor="#D0D0D0" width="300" align="center"'''Date'''<br />
 bgcolor="#A6B658" width="300" align="center"'''Speaker'''<br />
 bgcolor="#BCD2EE" width="300" align="center"'''Title (click to see abstract)'''<br />
<br />
 bgcolor="#E0E0E0" February 14<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 14 Fun with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 21<br />
 bgcolor="#C6D46E" Moisés Herradón Cueto<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 21 <math>\mathcal F</math>un with commutative groups]]<br />
<br />
 bgcolor="#E0E0E0" February 28<br />
 bgcolor="#C6D46E" Dima Arinkin<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#February 28 ODEs: algebraic vs analytic vs formal]]<br />
<br />
 bgcolor="#E0E0E0" March 7<br />
 bgcolor="#C6D46E" Vladimir Sotirov<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 7 Topology of Affine Schemes]]<br />
<br />
 bgcolor="#E0E0E0" March 14<br />
 bgcolor="#C6D46E" David Wagner<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 14 TBD]]<br />
<br />
 bgcolor="#E0E0E0" March 21<br />
 bgcolor="#C6D46E" Mao Li<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#March 21 D modules in prime characteristic]]<br />
<br />
 bgcolor="#E0E0E0" March 28<br />
 bgcolor="#C6D46E" Spring break<br />
 bgcolor="#BCE2FE" Whoo!<br />
<br />
 bgcolor="#E0E0E0" April 4<br />
 bgcolor="#C6D46E" Rachel Davis<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 4 TBD]]<br />
<br />
 bgcolor="#E0E0E0" April 11<br />
 bgcolor="#C6D46E" Brandon Boggess<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 11 TBD]]<br />
<br />
 bgcolor="#E0E0E0" April 18<br />
 bgcolor="#C6D46E" Soumya Sankar<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 18 TBD]]<br />
<br />
 bgcolor="#E0E0E0" April 25<br />
 bgcolor="#C6D46E" Solly Parenti<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#April 25 TBD]]<br />
<br />
 bgcolor="#E0E0E0" May 2<br />
 bgcolor="#C6D46E" TBD<br />
 bgcolor="#BCE2FE"[[Graduate Algebraic Geometry Seminar#May 2 TBD]]<br />
}<br />
</center><br />
<br />
== February 14 ==<br />
<center><br />
{ style="color:black; fontsize:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
<br />
 bgcolor="#A6B658" align="center" style="fontsize:125%"  '''Moisés Herradón Cueto'''<br />
<br />
 bgcolor="#BCD2EE" align="center"  Title: Fun with commutative groups<br />
<br />
