https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Djbruce&feedformat=atomMath - User contributions [en]2017-11-23T20:08:22ZUser contributionsMediaWiki 1.26.0https://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13798Graduate Algebraic Geometry Seminar2017-07-10T13:34:31Z<p>Djbruce: </p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| A gentle introduction to descent ]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 3<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| A gentle introduction to descent, part 2 ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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/maa-reviews/fundamental-algebraic-geometry-grothendiecks-fga-explained 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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar_Spring_2017&diff=13797Graduate Algebraic Geometry Seminar Spring 20172017-07-10T13:34:06Z<p>Djbruce: Created page with "''' '''When:''' Wednesdays 4:40pm '''Where:'''Van Vleck B321 (Spring 2017) Lizzie the OFFICIAL mascot of GAGS!! '''Who:''' YOU!! '''Why:'''..."</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| A gentle introduction to descent ]] <br />
|-<br />
| bgcolor="#E0E0E0"| May 3<br />
| bgcolor="#C6D46E"| Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| A gentle introduction to descent, part 2 ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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/maa-reviews/fundamental-algebraic-geometry-grothendiecks-fga-explained 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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13606Graduate Algebraic Geometry Seminar2017-04-03T12:32:14Z<p>Djbruce: /* February 15 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-Soderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Boij-Soderberg Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13605Graduate Algebraic Geometry Seminar2017-04-03T12:32:02Z<p>Djbruce: /* February 22 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-Soderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Boij-Soderberg Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13604Graduate Algebraic Geometry Seminar2017-04-03T12:31:48Z<p>Djbruce: /* March 15 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-Soderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Boij-Soderberg Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13603Graduate Algebraic Geometry Seminar2017-04-03T12:31:14Z<p>Djbruce: /* April 5 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-Soderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Boij-Soderberg Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13602Graduate Algebraic Geometry Seminar2017-04-03T12:30:58Z<p>Djbruce: /* March 15 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-Soderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Boij-Soderberg Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13601Graduate Algebraic Geometry Seminar2017-04-03T12:30:44Z<p>Djbruce: /* Spring 2017 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| Picard groups of moduli problems II]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| Adjoint functors rule your life]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| Wendy Cheng<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| Boij-Soderberg Theory]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wendy Cheng'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Boij-Soderberg Theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13517Graduate Algebraic Geometry Seminar2017-03-15T19:21:36Z<p>Djbruce: /* March 15 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13516Graduate Algebraic Geometry Seminar2017-03-15T19:21:09Z<p>Djbruce: /* Spring 2017 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| We Failed, We All Failed Pt. 3]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13483Graduate Algebraic Geometry Seminar2017-03-08T21:16:20Z<p>Djbruce: /* April 5 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Wiltshire-Gordon'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13482Graduate Algebraic Geometry Seminar2017-03-08T21:16:05Z<p>Djbruce: /* Spring 2017 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| Picard groups of moduli problems]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| John Wiltshire-Gordon<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13467Madison Math Circle Abstracts2017-03-05T17:41:04Z<p>Djbruce: /* March 20 2017 (East) */</p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
</center><br />
<br />
== February 13 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Solve it with colors'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!)<br />
We will look at problems that can be solved by a clever coloring design. <br />
|}<br />
</center><br />
<br />
<br />
== February 20 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Reese Johnston'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Knights and Knaves'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
An ancient Greek philosopher Epimenides famously said "All Cretans are liars". Ignoring for a moment the fact that Epimenides himself was from Crete, what would happen if he was right? How could we get information from people who always lie? Or, worse, what if among these lying "knaves" are some truthful "knights"? How could we tell which is which? Using some tools from logic, we'll explore this and some other questions of the same sort.<br />
|}<br />
</center><br />
<br />
== February 27 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jessica Lin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The Mathematics Behind Sound'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will explore the mathematics behind soundwaves. This will include dissecting the structure of soundwaves, understanding why they create certain tones, and discovering how sound cancelling headphones work. If time permits, we may even talk about whether you can "hear the shape of a drum."<br />
|}<br />
</center><br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!<br />
|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|}<br />
</center><br />
<br />
== March 20 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Doodling Daydreams'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
As a high schooler I occasionally got bored, would zone out, and would doodle on my paper. Often repeatedly tracing around something on my paper creating doodles like this:<br />
<gallery widths=300px heights=150px mode="packed"><br />
File:doodle.jpg<br />
</gallery><br />
<br />
In this bored state my mind would often wander, and I would wonder about important things like "Will I have a date for prom?" or "What is the cafeteria serving for lunch?", but germane to this talk were my wonderings about, "What’s happening to the shape of this doodle?" It turns out that these idle daydreams and doodles provide a good taste for how mathematicians "do" math. We will start by doodling and asking questions, and then we'll see where these lead us mathematically.<br />
|} <br />
</center><br />
<br />
== April 3 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|}<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13466Madison Math Circle Abstracts2017-03-05T17:38:32Z<p>Djbruce: /* March 20 2017 (East) */</p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
</center><br />
<br />
== February 13 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Solve it with colors'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!)<br />
We will look at problems that can be solved by a clever coloring design. <br />
|}<br />
</center><br />
<br />
<br />
== February 20 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Reese Johnston'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Knights and Knaves'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
An ancient Greek philosopher Epimenides famously said "All Cretans are liars". Ignoring for a moment the fact that Epimenides himself was from Crete, what would happen if he was right? How could we get information from people who always lie? Or, worse, what if among these lying "knaves" are some truthful "knights"? How could we tell which is which? Using some tools from logic, we'll explore this and some other questions of the same sort.<br />
|}<br />
</center><br />
<br />
== February 27 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jessica Lin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The Mathematics Behind Sound'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will explore the mathematics behind soundwaves. This will include dissecting the structure of soundwaves, understanding why they create certain tones, and discovering how sound cancelling headphones work. If time permits, we may even talk about whether you can "hear the shape of a drum."<br />
|}<br />
</center><br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!<br />
|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|}<br />
</center><br />
<br />
== March 20 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Doodling Daydreams'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
As a high schooler I occasionally got bored, would zone out, and would doodle on my paper. Often repeatedly tracing around some something on my paper making doodles like this:<br />
<gallery widths=300px heights=150px mode="packed"><br />
File:doodle.jpg<br />
</gallery><br />
<br />
In this bored state my mind would often wander, and I would wonder about important things like "Will I have a date for prom?" or "What is the cafeteria serving for lunch?", but germane to this talk were my wondering about, "What happens to the shape of this doodle?" It turns out that these idle daydream and doodles provide a good taste for how mathematicians "do" math. We will start by doodling and asking questions, and then we'll see where these lead us mathematically.<br />
|} <br />
</center><br />
<br />
== April 3 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|}<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=13465Madison Math Circle2017-03-05T17:29:24Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<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.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <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/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.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_2hmb6vtDUfRonNb '''Math Circle Registration Form''']<br />
<br />
All of you 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 UW-Madison 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; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</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 UW-Madison 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 join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of three professors and three graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. 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: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:djbruce.jpg|[http://www.math.wisc.edu/~djbruce/ DJ 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 record-keeping, 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 2016 and Spring 2017=<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; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2016 <br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| <span style="color:red">August 6, 2016 <br> (Click Title for Time & Location.)</span> || [https://discovery.wisc.edu/programs/saturday-science Science Saturday] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#August_6_2016 Game Busters]<br />
|-<br />
| September 12, 2016 || [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_12_2016 Why do my earbuds keep getting entangled?]<br />
|-<br />
| September 19, 2016 || [http://www.math.wisc.edu/~djbruce/ DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_19_2016 Is Any Knot Not the Unkont? ] <br />
|-<br />
| September 26, 2016 || [http://mmaguire.weebly.com/ Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_26_2016 Coloring Maps] <br />
|-<br />
| October 3, 2016 || [http://www.math.wisc.edu/~zcharles/ Zach Charles] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_3_2016 1 + 1 = 10, or How does my smartphone do anything?] <br />
|-<br />
| October 10, 2016 || [http://www.math.wisc.edu/~jkrush/ Keith Rush] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_10_2016 Randomness, determinism and approximation: a historical question] <br />
|-<br />
| October 17, 2016 || [http://www.math.wisc.edu/~pmwood/ Phillip Matchett-Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016 The game of Criss-Cross]<br />
|-<br />
| October 24, 2016 || Ethan Biehl || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016 A Chocolate Bar for Every Real Number] <br />
|-<br />
| October 31, 2016 || No Meeting || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016 Enjoy Halloween!] <br />
|-<br />
| November 7, 2016 || [https://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_7_2016 Are we there yet?] <br />
|-<br />
| November 14, 2016 || [http://www.math.wisc.edu/~micky/ Micky Soule Steinberg] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_14_2016 Circles and Triangles] <br />
|-<br />
| November 21, 2016 || [https://www.math.wisc.edu/~valko/ Benedek Valko] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_21_2016 Fun with hats] <br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
|January 30, 2017 || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#January_30_2017 The Josephus Problem] <br />
|-<br />
| February 6, 2017 || Cullen McDonald || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_6_2017 Building a 4-dimensional house] <br />
|-<br />
| February 13, 2017 || Dima Arinkin || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017 Solve it with colors] <br />
|-<br />
| February 20, 2017 || Reese Johnston || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017 Knights and Knaves] <br />
|-<br />
| February 27, 2017 || [https://www.math.wisc.edu/~jessica/ Jessica Lin] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_27_2017 The Mathematics Behind Sound] <br />
|-<br />
| March 6, 2017 || Becky Eastham || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_6_2017 How to Win a Brand New Car and Escape Execution with Probability] <br />
|-<br />
| March 13, 2017 || Jim Brunner || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_13_2017 TBD] <br />
|-<br />
| March 20, 2017 || No Meeting - (UW Spring Break) || <br />
|-<br />
| March 27, 2017 || John Wiltshire-Gordon || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_27_2017 TBD] <br />
|-<br />
| April 3, 2017 || Will Mitchell || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017 TBD] <br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=High School Meetings=<br />
<br />
We are experimenting with holding some Math Circle meetings directly at local high schools. Our schedule for the fall is below. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2016<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| October 17, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~derman Daniel Erman] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016_.28JMM.29 What does math research look like?] ||<br />
|-<br />
| October 24, 2016 || 2:45pm West High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016_.28West.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| October 31, 2016 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016.28East.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| December 5, 2016 || 2:45pm East High || [http://www.math.wisc.edu/~andrews/ Uri Andrews] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28East.29 How to split an apartment] ||<br />
|-<br />
| December 5, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~pmwood Phillip Matchett Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28JMM.29 The game of Criss-Cross] ||<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| February 13, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~evaelduque Eva Elduque] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017_.28East.29 Pick's Theorem] ||<br />
|-<br />
| February 20, 2017 || 2:45pm JMM || [https://www.math.wisc.edu/~mmaguire2 Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017_.28JMM.29 Coloring Maps] ||<br />
|-<br />
| March 20, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_20_2017_.28East.29 Doodling Daydreams] ||<br />
|-<br />
| April 3rd, 2017 || 2:45pm JMM || [http://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017_.28JMM.29 Are we there yet?] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 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/lesson-plans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=13464Madison Math Circle2017-03-05T17:28:46Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<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.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <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/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.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_2hmb6vtDUfRonNb '''Math Circle Registration Form''']<br />
<br />
All of you 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 UW-Madison 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; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</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 UW-Madison 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 join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of three professors and three graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. 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: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:djbruce.jpg|[http://www.math.wisc.edu/~djbruce/ DJ 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 record-keeping, 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 2016 and Spring 2017=<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; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2016 <br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| <span style="color:red">August 6, 2016 <br> (Click Title for Time & Location.)</span> || [https://discovery.wisc.edu/programs/saturday-science Science Saturday] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#August_6_2016 Game Busters]<br />
|-<br />
| September 12, 2016 || [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_12_2016 Why do my earbuds keep getting entangled?]<br />
|-<br />
| September 19, 2016 || [http://www.math.wisc.edu/~djbruce/ DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_19_2016 Is Any Knot Not the Unkont? ] <br />
|-<br />
| September 26, 2016 || [http://mmaguire.weebly.com/ Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_26_2016 Coloring Maps] <br />
|-<br />
| October 3, 2016 || [http://www.math.wisc.edu/~zcharles/ Zach Charles] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_3_2016 1 + 1 = 10, or How does my smartphone do anything?] <br />
|-<br />
| October 10, 2016 || [http://www.math.wisc.edu/~jkrush/ Keith Rush] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_10_2016 Randomness, determinism and approximation: a historical question] <br />
|-<br />
| October 17, 2016 || [http://www.math.wisc.edu/~pmwood/ Phillip Matchett-Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016 The game of Criss-Cross]<br />
|-<br />
| October 24, 2016 || Ethan Biehl || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016 A Chocolate Bar for Every Real Number] <br />
|-<br />
| October 31, 2016 || No Meeting || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016 Enjoy Halloween!] <br />
|-<br />
| November 7, 2016 || [https://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_7_2016 Are we there yet?] <br />
|-<br />
| November 14, 2016 || [http://www.math.wisc.edu/~micky/ Micky Soule Steinberg] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_14_2016 Circles and Triangles] <br />
|-<br />
| November 21, 2016 || [https://www.math.wisc.edu/~valko/ Benedek Valko] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_21_2016 Fun with hats] <br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
|January 30, 2017 || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#January_30_2017 The Josephus Problem] <br />
|-<br />
| February 6, 2017 || Cullen McDonald || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_6_2017 Building a 4-dimensional house] <br />
|-<br />
| February 13, 2017 || Dima Arinkin || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017 Solve it with colors] <br />
|-<br />
| February 20, 2017 || Reese Johnston || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017 Knights and Knaves] <br />
|-<br />
| February 27, 2017 || [https://www.math.wisc.edu/~jessica/ Jessica Lin] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_27_2017 The Mathematics Behind Sound] <br />
|-<br />
| March 6, 2017 || Becky Eastham || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_6_2017 How to Win a Brand New Car and Escape Execution with Probability] <br />
|-<br />
| March 13, 2017 || Jim Brunner || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_13_2017 TBD] <br />
|-<br />
| March 20, 2017 || No Meeting - (UW Spring Break) || <br />
|-<br />
| March 27, 2017 || John Wiltshire-Gordon || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_27_2017 TBD] <br />
|-<br />
| April 3, 2017 || Will Mitchell || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017 TBD] <br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=High School Meetings=<br />
<br />
We are experimenting with holding some Math Circle meetings directly at local high schools. Our schedule for the fall is below. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2016<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| October 17, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~derman Daniel Erman] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016_.28JMM.29 What does math research look like?] ||<br />
|-<br />
| October 24, 2016 || 2:45pm West High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016_.28West.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| October 31, 2016 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016.28East.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| December 5, 2016 || 2:45pm East High || [http://www.math.wisc.edu/~andrews/ Uri Andrews] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28East.29 How to split an apartment] ||<br />
|-<br />
| December 5, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~pmwood Phillip Matchett Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28JMM.29 The game of Criss-Cross] ||<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| February 13, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~evaelduque Eva Elduque] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017_.28East.29 Pick's Theorem] ||<br />
|-<br />
| February 20, 2017 || 2:45pm JMM || [https://www.math.wisc.edu/~mmaguire2 Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017_.28JMM.29 Coloring Maps] ||<br />
|-<br />
| March 20, 2017 || 2:45pm East High || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_20_2017_.28East.29 Doodling Daydreams] ||<br />
|-<br />
| April 3rd, 2017 || 2:45pm JMM || [http://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017_.28JMM.29 Are we there yet?] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 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/lesson-plans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13463Madison Math Circle Abstracts2017-03-05T17:26:35Z<p>Djbruce: /* March 20 2017 (East) */</p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
</center><br />
<br />
== February 13 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Solve it with colors'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!)<br />
We will look at problems that can be solved by a clever coloring design. <br />
|}<br />
</center><br />
<br />
<br />
== February 20 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Reese Johnston'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Knights and Knaves'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
An ancient Greek philosopher Epimenides famously said "All Cretans are liars". Ignoring for a moment the fact that Epimenides himself was from Crete, what would happen if he was right? How could we get information from people who always lie? Or, worse, what if among these lying "knaves" are some truthful "knights"? How could we tell which is which? Using some tools from logic, we'll explore this and some other questions of the same sort.<br />
|}<br />
</center><br />
<br />
== February 27 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jessica Lin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The Mathematics Behind Sound'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will explore the mathematics behind soundwaves. This will include dissecting the structure of soundwaves, understanding why they create certain tones, and discovering how sound cancelling headphones work. If time permits, we may even talk about whether you can "hear the shape of a drum."<br />
|}<br />
</center><br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!<br />
|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|}<br />
</center><br />
<br />
== March 20 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Doodling Daydreams'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
As a high schooler I occasionally got bored, would zone out, and doodle on my paper. Often I would repeatedly trace around some something on my paper making doodles like this:<br />
<br />
<gallery widths=300px heights=150px mode="packed"><br />
File:doodle.jpg<br />
</gallery><br />
<br />
In my boredom I would often wonder about things like "Will I have a date for prom?" or "What is the cafeteria serving for lunch today?", but germane to this talk were my wondering about, "What happens to the shape of this doodle?" It turns out that these idle daydream and doodles provide an good taste for how mathematicians "do" math. We will start by doodling and asking questions, and will see where these lead us mathematically.<br />
|} <br />
</center><br />
<br />
== April 3 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|}<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13462Madison Math Circle Abstracts2017-03-05T17:25:24Z<p>Djbruce: /* March 20 2017 (East) */</p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
</center><br />
<br />
== February 13 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Solve it with colors'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!)<br />
We will look at problems that can be solved by a clever coloring design. <br />
|}<br />
</center><br />
<br />
<br />
== February 20 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Reese Johnston'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Knights and Knaves'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
An ancient Greek philosopher Epimenides famously said "All Cretans are liars". Ignoring for a moment the fact that Epimenides himself was from Crete, what would happen if he was right? How could we get information from people who always lie? Or, worse, what if among these lying "knaves" are some truthful "knights"? How could we tell which is which? Using some tools from logic, we'll explore this and some other questions of the same sort.<br />
|}<br />
</center><br />
<br />
== February 27 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jessica Lin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The Mathematics Behind Sound'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will explore the mathematics behind soundwaves. This will include dissecting the structure of soundwaves, understanding why they create certain tones, and discovering how sound cancelling headphones work. If time permits, we may even talk about whether you can "hear the shape of a drum."<br />
|}<br />
</center><br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!<br />
|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|}<br />
</center><br />
<br />
== March 20 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Doodling Daydreams'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
As a high schooler I occasionally got bored and would zone out and doodle on my paper. Often I would repeatedly trace around some something on my paper making doodles like this:<br />
<br />
<gallery widths=300px heights=150px mode="packed"><br />
File:doodle.jpg<br />
</gallery><br />
<br />
In my boredom I would often wonder about things like "Will I have a date for prom" or "What is the cafeteria serving for lunch today?", but germane to this talk were my wondering about, "What happens to the shape of this doodle?" It turns out that these idle daydream and doodles provide an good taste for how mathematicians "do" math. We will start by doodling and asking questions, and see where these lead us mathematically.<br />
|} <br />
</center><br />
<br />
== April 3 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|}<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13461Madison Math Circle Abstracts2017-03-05T17:25:08Z<p>Djbruce: /* March 20 2017 (East) */</p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
</center><br />
<br />
== February 13 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Solve it with colors'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!)<br />
We will look at problems that can be solved by a clever coloring design. <br />
|}<br />
</center><br />
<br />
<br />
== February 20 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Reese Johnston'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Knights and Knaves'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
An ancient Greek philosopher Epimenides famously said "All Cretans are liars". Ignoring for a moment the fact that Epimenides himself was from Crete, what would happen if he was right? How could we get information from people who always lie? Or, worse, what if among these lying "knaves" are some truthful "knights"? How could we tell which is which? Using some tools from logic, we'll explore this and some other questions of the same sort.<br />
|}<br />
</center><br />
<br />
== February 27 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jessica Lin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The Mathematics Behind Sound'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will explore the mathematics behind soundwaves. This will include dissecting the structure of soundwaves, understanding why they create certain tones, and discovering how sound cancelling headphones work. If time permits, we may even talk about whether you can "hear the shape of a drum."<br />
|}<br />
</center><br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!<br />
|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|}<br />
</center><br />
<br />
== March 20 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Doodling Daydreams'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
As a high schooler I occasionally got board and would zone out and doodle on my paper. Often I would repeatedly trace around some something on my paper making doodles like this:<br />
<br />
<gallery widths=300px heights=150px mode="packed"><br />
File:doodle.jpg<br />
</gallery><br />
<br />
In my boredom I would often wonder about things like "Will I have a date for prom" or "What is the cafeteria serving for lunch today?", but germane to this talk were my wondering about, "What happens to the shape of this doodle?" It turns out that these idle daydream and doodles provide an good taste for how mathematicians "do" math. We will start by doodling and asking questions, and see where these lead us mathematically.<br />
|} <br />
</center><br />
<br />
== April 3 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|}<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13460Madison Math Circle Abstracts2017-03-05T17:24:48Z<p>Djbruce: /* March 20 2017 (East) */</p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
</center><br />
<br />
== February 13 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Solve it with colors'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!)<br />
We will look at problems that can be solved by a clever coloring design. <br />
|}<br />
</center><br />
<br />
<br />
== February 20 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Reese Johnston'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Knights and Knaves'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
An ancient Greek philosopher Epimenides famously said "All Cretans are liars". Ignoring for a moment the fact that Epimenides himself was from Crete, what would happen if he was right? How could we get information from people who always lie? Or, worse, what if among these lying "knaves" are some truthful "knights"? How could we tell which is which? Using some tools from logic, we'll explore this and some other questions of the same sort.<br />
|}<br />
</center><br />
<br />
== February 27 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jessica Lin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The Mathematics Behind Sound'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will explore the mathematics behind soundwaves. This will include dissecting the structure of soundwaves, understanding why they create certain tones, and discovering how sound cancelling headphones work. If time permits, we may even talk about whether you can "hear the shape of a drum."<br />
|}<br />
</center><br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!<br />
|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|}<br />
</center><br />
<br />
== March 20 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Doodling Daydreams'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
As a high schooler I occasionally got board and would zone out and doodle on my paper. Often I would repeatedly trace around some something on my paper making doodles like this:<br />
<br />
<gallery widths=300px heights=250px mode="packed"><br />
File:doodle.jpg<br />
</gallery><br />
<br />
In my boredom I would often wonder about things like "Will I have a date for prom" or "What is the cafeteria serving for lunch today?", but germane to this talk were my wondering about, "What happens to the shape of this doodle?" It turns out that these idle daydream and doodles provide an good taste for how mathematicians "do" math. We will start by doodling and asking questions, and see where these lead us mathematically.<br />
|} <br />
</center><br />
<br />
== April 3 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|}<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=File:Doodle.jpg&diff=13459File:Doodle.jpg2017-03-05T17:22:55Z<p>Djbruce: </p>
<hr />
<div></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13458Madison Math Circle Abstracts2017-03-05T17:22:27Z<p>Djbruce: /* March 20 2017 (East) */</p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
</center><br />
<br />
== February 13 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Solve it with colors'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!)<br />
We will look at problems that can be solved by a clever coloring design. <br />
|}<br />
</center><br />
<br />
<br />
== February 20 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Reese Johnston'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Knights and Knaves'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
An ancient Greek philosopher Epimenides famously said "All Cretans are liars". Ignoring for a moment the fact that Epimenides himself was from Crete, what would happen if he was right? How could we get information from people who always lie? Or, worse, what if among these lying "knaves" are some truthful "knights"? How could we tell which is which? Using some tools from logic, we'll explore this and some other questions of the same sort.<br />
|}<br />
</center><br />
<br />
== February 27 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jessica Lin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The Mathematics Behind Sound'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will explore the mathematics behind soundwaves. This will include dissecting the structure of soundwaves, understanding why they create certain tones, and discovering how sound cancelling headphones work. If time permits, we may even talk about whether you can "hear the shape of a drum."<br />
|}<br />
</center><br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!<br />
|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|}<br />
</center><br />
<br />
== March 20 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Doodling Daydreams'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
As a high schooler I occasionally got board and would zone out and doodle on my paper. Often I would repeatedly trace around some something on my paper making doodles like this:<br />
[[File:doodle.jpg]]<br />
In my boredom I would often wonder about things like "Will I have a date for prom" or "What is the cafeteria serving for lunch today?", but germane to this talk were my wondering about, "What happens to the shape of this doodle?" It turns out that these idle daydream and doodles provide an good taste for how mathematicians "do" math. We will start by doodling and asking questions, and see where these lead us mathematically.<br />
|} <br />
</center><br />
<br />
== April 3 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|}<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13457Madison Math Circle Abstracts2017-03-05T17:22:05Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
</center><br />
<br />
== February 13 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Solve it with colors'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!)<br />
We will look at problems that can be solved by a clever coloring design. <br />
|}<br />
</center><br />
<br />
<br />
== February 20 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Reese Johnston'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Knights and Knaves'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
An ancient Greek philosopher Epimenides famously said "All Cretans are liars". Ignoring for a moment the fact that Epimenides himself was from Crete, what would happen if he was right? How could we get information from people who always lie? Or, worse, what if among these lying "knaves" are some truthful "knights"? How could we tell which is which? Using some tools from logic, we'll explore this and some other questions of the same sort.<br />
|}<br />
</center><br />
<br />
== February 27 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jessica Lin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The Mathematics Behind Sound'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will explore the mathematics behind soundwaves. This will include dissecting the structure of soundwaves, understanding why they create certain tones, and discovering how sound cancelling headphones work. If time permits, we may even talk about whether you can "hear the shape of a drum."<br />
|}<br />
</center><br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!<br />
|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|}<br />
</center><br />
<br />
== March 20 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Doodling Daydreams'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
As a high schooler I occasionally got board and would zone out and doodle on my paper. Often I would repeatedly trace around some something on my paper making doodles like this:<br />
<br />
In my boredom I would often wonder about things like "Will I have a date for prom" or "What is the cafeteria serving for lunch today?", but germane to this talk were my wondering about, "What happens to the shape of this doodle?" It turns out that these idle daydream and doodles provide an good taste for how mathematicians "do" math. We will start by doodling and asking questions, and see where these lead us mathematically.<br />
|} <br />
</center><br />
<br />
== April 3 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|}<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13456Madison Math Circle Abstracts2017-03-05T17:20:46Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
</center><br />
<br />
== February 13 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Solve it with colors'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!)<br />
We will look at problems that can be solved by a clever coloring design. <br />
|}<br />
</center><br />
<br />
<br />
== February 20 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Reese Johnston'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Knights and Knaves'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
An ancient Greek philosopher Epimenides famously said "All Cretans are liars". Ignoring for a moment the fact that Epimenides himself was from Crete, what would happen if he was right? How could we get information from people who always lie? Or, worse, what if among these lying "knaves" are some truthful "knights"? How could we tell which is which? Using some tools from logic, we'll explore this and some other questions of the same sort.<br />
|}<br />
</center><br />
<br />
== February 27 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jessica Lin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The Mathematics Behind Sound'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will explore the mathematics behind soundwaves. This will include dissecting the structure of soundwaves, understanding why they create certain tones, and discovering how sound cancelling headphones work. If time permits, we may even talk about whether you can "hear the shape of a drum."<br />
|}<br />
</center><br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!<br />
|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|}<br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Doodling Daydreams'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
As a high schooler I occasionally got board and would zone out and doodle on my paper. Often I would repeatedly trace around some something on my paper making doodles like this:<br />
<br />
In my boredom I would often wonder about things like "Will I have a date for prom" or "What is the cafeteria serving for lunch today?", but germane to this talk were my wondering about, "What happens to the shape of this doodle?" It turns out that these idle daydream and doodles provide an good taste for how mathematicians "do" math. We will start by doodling and asking questions, and see where these lead us mathematically.} <br />
</center><br />
<br />
== April 3 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|}<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=13455Madison Math Circle2017-03-05T17:06:41Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<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.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <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/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.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_2hmb6vtDUfRonNb '''Math Circle Registration Form''']<br />
<br />
All of you 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 UW-Madison 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; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</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 UW-Madison 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 join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of three professors and three graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. 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: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:djbruce.jpg|[http://www.math.wisc.edu/~djbruce/ DJ 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 record-keeping, 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 2016 and Spring 2017=<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; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2016 <br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| <span style="color:red">August 6, 2016 <br> (Click Title for Time & Location.)</span> || [https://discovery.wisc.edu/programs/saturday-science Science Saturday] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#August_6_2016 Game Busters]<br />
|-<br />
| September 12, 2016 || [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_12_2016 Why do my earbuds keep getting entangled?]<br />
|-<br />
| September 19, 2016 || [http://www.math.wisc.edu/~djbruce/ DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_19_2016 Is Any Knot Not the Unkont? ] <br />
|-<br />
| September 26, 2016 || [http://mmaguire.weebly.com/ Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_26_2016 Coloring Maps] <br />
|-<br />
| October 3, 2016 || [http://www.math.wisc.edu/~zcharles/ Zach Charles] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_3_2016 1 + 1 = 10, or How does my smartphone do anything?] <br />
|-<br />
| October 10, 2016 || [http://www.math.wisc.edu/~jkrush/ Keith Rush] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_10_2016 Randomness, determinism and approximation: a historical question] <br />
|-<br />
| October 17, 2016 || [http://www.math.wisc.edu/~pmwood/ Phillip Matchett-Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016 The game of Criss-Cross]<br />
|-<br />
| October 24, 2016 || Ethan Biehl || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016 A Chocolate Bar for Every Real Number] <br />
|-<br />
| October 31, 2016 || No Meeting || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016 Enjoy Halloween!] <br />
|-<br />
| November 7, 2016 || [https://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_7_2016 Are we there yet?] <br />
|-<br />
| November 14, 2016 || [http://www.math.wisc.edu/~micky/ Micky Soule Steinberg] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_14_2016 Circles and Triangles] <br />
|-<br />
| November 21, 2016 || [https://www.math.wisc.edu/~valko/ Benedek Valko] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_21_2016 Fun with hats] <br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
|January 30, 2017 || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#January_30_2017 The Josephus Problem] <br />
|-<br />
| February 6, 2017 || Cullen McDonald || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_6_2017 Building a 4-dimensional house] <br />
|-<br />
| February 13, 2017 || Dima Arinkin || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017 Solve it with colors] <br />
|-<br />
| February 20, 2017 || Reese Johnston || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017 Knights and Knaves] <br />
|-<br />
| February 27, 2017 || [https://www.math.wisc.edu/~jessica/ Jessica Lin] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_27_2017 The Mathematics Behind Sound] <br />
|-<br />
| March 6, 2017 || Becky Eastham || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_6_2017 How to Win a Brand New Car and Escape Execution with Probability] <br />
|-<br />
| March 13, 2017 || Jim Brunner || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_13_2017 TBD] <br />
|-<br />
| March 20, 2017 || No Meeting - (UW Spring Break) || <br />
|-<br />
| March 27, 2017 || John Wiltshire-Gordon || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_27_2017 TBD] <br />
|-<br />
| April 3, 2017 || Will Mitchell || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017 TBD] <br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=High School Meetings=<br />
<br />
We are experimenting with holding some Math Circle meetings directly at local high schools. Our schedule for the fall is below. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2016<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| October 17, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~derman Daniel Erman] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016_.28JMM.29 What does math research look like?] ||<br />
|-<br />
| October 24, 2016 || 2:45pm West High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016_.28West.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| October 31, 2016 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016.28East.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| December 5, 2016 || 2:45pm East High || [http://www.math.wisc.edu/~andrews/ Uri Andrews] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28East.29 How to split an apartment] ||<br />
|-<br />
| December 5, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~pmwood Phillip Matchett Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28JMM.29 The game of Criss-Cross] ||<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| February 13, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~evaelduque Eva Elduque] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017_.28East.29 Pick's Theorem] ||<br />
|-<br />
| February 20, 2017 || 2:45pm JMM || [https://www.math.wisc.edu/~mmaguire2 Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017_.28JMM.29 Coloring Maps] ||<br />
|-<br />
| March 20, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstract#March_20_2017_.28East.29 Doodling Daydreams] ||<br />
|-<br />
| April 3rd, 2017 || 2:45pm JMM || [http://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017_.28JMM.29 Are we there yet?] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 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/lesson-plans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=13454Madison Math Circle2017-03-05T17:06:13Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<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.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <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/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.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_2hmb6vtDUfRonNb '''Math Circle Registration Form''']<br />
<br />
All of you 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 UW-Madison 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; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</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 UW-Madison 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 join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of three professors and three graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. 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: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:djbruce.jpg|[http://www.math.wisc.edu/~djbruce/ DJ 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 record-keeping, 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 2016 and Spring 2017=<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; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2016 <br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| <span style="color:red">August 6, 2016 <br> (Click Title for Time & Location.)</span> || [https://discovery.wisc.edu/programs/saturday-science Science Saturday] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#August_6_2016 Game Busters]<br />
|-<br />
| September 12, 2016 || [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_12_2016 Why do my earbuds keep getting entangled?]<br />
|-<br />
| September 19, 2016 || [http://www.math.wisc.edu/~djbruce/ DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_19_2016 Is Any Knot Not the Unkont? ] <br />
|-<br />
| September 26, 2016 || [http://mmaguire.weebly.com/ Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_26_2016 Coloring Maps] <br />
|-<br />
| October 3, 2016 || [http://www.math.wisc.edu/~zcharles/ Zach Charles] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_3_2016 1 + 1 = 10, or How does my smartphone do anything?] <br />
|-<br />
| October 10, 2016 || [http://www.math.wisc.edu/~jkrush/ Keith Rush] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_10_2016 Randomness, determinism and approximation: a historical question] <br />
|-<br />
| October 17, 2016 || [http://www.math.wisc.edu/~pmwood/ Phillip Matchett-Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016 The game of Criss-Cross]<br />
|-<br />
| October 24, 2016 || Ethan Biehl || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016 A Chocolate Bar for Every Real Number] <br />
|-<br />
| October 31, 2016 || No Meeting || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016 Enjoy Halloween!] <br />
|-<br />
| November 7, 2016 || [https://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_7_2016 Are we there yet?] <br />
|-<br />
| November 14, 2016 || [http://www.math.wisc.edu/~micky/ Micky Soule Steinberg] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_14_2016 Circles and Triangles] <br />
|-<br />
| November 21, 2016 || [https://www.math.wisc.edu/~valko/ Benedek Valko] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_21_2016 Fun with hats] <br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
|January 30, 2017 || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#January_30_2017 The Josephus Problem] <br />
|-<br />
| February 6, 2017 || Cullen McDonald || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_6_2017 Building a 4-dimensional house] <br />
|-<br />
| February 13, 2017 || Dima Arinkin || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017 Solve it with colors] <br />
|-<br />
| February 20, 2017 || Reese Johnston || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017 Knights and Knaves] <br />
|-<br />
| February 27, 2017 || [https://www.math.wisc.edu/~jessica/ Jessica Lin] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_27_2017 The Mathematics Behind Sound] <br />
|-<br />
| March 6, 2017 || Becky Eastham || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_6_2017 How to Win a Brand New Car and Escape Execution with Probability] <br />
|-<br />
| March 13, 2017 || Jim Brunner || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_13_2017 TBD] <br />
|-<br />
| March 20, 2017 || No Meeting - (UW Spring Break) || <br />
|-<br />
| March 27, 2017 || John Wiltshire-Gordon || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_27_2017 TBD] <br />
|-<br />
| April 3, 2017 || Will Mitchell || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017 TBD] <br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=High School Meetings=<br />
<br />
We are experimenting with holding some Math Circle meetings directly at local high schools. Our schedule for the fall is below. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2016<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| October 17, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~derman Daniel Erman] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016_.28JMM.29 What does math research look like?] ||<br />
|-<br />
| October 24, 2016 || 2:45pm West High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016_.28West.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| October 31, 2016 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016.28East.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| December 5, 2016 || 2:45pm East High || [http://www.math.wisc.edu/~andrews/ Uri Andrews] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28East.29 How to split an apartment] ||<br />
|-<br />
| December 5, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~pmwood Phillip Matchett Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28JMM.29 The game of Criss-Cross] ||<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| February 13, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~evaelduque Eva Elduque] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017_.28East.29 Pick's Theorem] ||<br />
|-<br />
| February 20, 2017 || 2:45pm JMM || [https://www.math.wisc.edu/~mmaguire2 Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017_.28JMM.29 Coloring Maps] ||<br />
|-<br />
| March 20, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || <br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstract#March_20_2017_.28East.29 Doodling Daydreams] ||<br />
|-<br />
| April 3rd, 2017 || 2:45pm JMM || [http://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017_.28JMM.29 Are we there yet?] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 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/lesson-plans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13433Graduate Algebraic Geometry Seminar2017-02-27T20:42:20Z<p>Djbruce: /* February 22 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13432Graduate Algebraic Geometry Seminar2017-02-27T20:42:02Z<p>Djbruce: /* February 15 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''n/a'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: No Talk<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: n/a<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13431Graduate Algebraic Geometry Seminar2017-02-27T20:41:45Z<p>Djbruce: /* March 1 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13430Graduate Algebraic Geometry Seminar2017-02-27T20:41:03Z<p>Djbruce: /* Spring 2017 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed Pt. 2]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | An Introduction to Mori's Program]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13428Graduate Algebraic Geometry Seminar2017-02-27T19:47:58Z<p>Djbruce: /* Spring 2017 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=13397Madison Math Circle2017-02-19T17:37:10Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<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.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <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/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.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_2hmb6vtDUfRonNb '''Math Circle Registration Form''']<br />
<br />
All of you 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 UW-Madison 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; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</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 UW-Madison 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 join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of three professors and three graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. 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: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:djbruce.jpg|[http://www.math.wisc.edu/~djbruce/ DJ 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 />
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 record-keeping, 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 2016 and Spring 2017=<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; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2016 <br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| <span style="color:red">August 6, 2016 <br> (Click Title for Time & Location.)</span> || [https://discovery.wisc.edu/programs/saturday-science Science Saturday] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#August_6_2016 Game Busters]<br />
|-<br />
| September 12, 2016 || [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_12_2016 Why do my earbuds keep getting entangled?]<br />
|-<br />
| September 19, 2016 || [http://www.math.wisc.edu/~djbruce/ DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_19_2016 Is Any Knot Not the Unkont? ] <br />
|-<br />
| September 26, 2016 || [http://mmaguire.weebly.com/ Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_26_2016 Coloring Maps] <br />
|-<br />
| October 3, 2016 || [http://www.math.wisc.edu/~zcharles/ Zach Charles] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_3_2016 1 + 1 = 10, or How does my smartphone do anything?] <br />
|-<br />
| October 10, 2016 || [http://www.math.wisc.edu/~jkrush/ Keith Rush] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_10_2016 Randomness, determinism and approximation: a historical question] <br />
|-<br />
| October 17, 2016 || [http://www.math.wisc.edu/~pmwood/ Phillip Matchett-Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016 The game of Criss-Cross]<br />
|-<br />
| October 24, 2016 || Ethan Biehl || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016 A Chocolate Bar for Every Real Number] <br />
|-<br />
| October 31, 2016 || No Meeting || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016 Enjoy Halloween!] <br />
|-<br />
| November 7, 2016 || [https://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_7_2016 Are we there yet?] <br />
|-<br />
| November 14, 2016 || [http://www.math.wisc.edu/~micky/ Micky Soule Steinberg] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_14_2016 Circles and Triangles] <br />
|-<br />
| November 21, 2016 || [https://www.math.wisc.edu/~valko/ Benedek Valko] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_21_2016 Fun with hats] <br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
|January 30, 2017 || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#January_30_2017 The Josephus Problem] <br />
|-<br />
| February 6, 2017 || Cullen McDonald || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_6_2017 Building a 4-dimensional house] <br />
|-<br />
| February 13, 2017 || Dima Arinkin || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017 Solve it with colors] <br />
|-<br />
| February 20, 2017 || Reese Johnston || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017 Knights and Knaves] <br />
|-<br />
| February 27, 2017 || [https://www.math.wisc.edu/~jessica/ Jessica Lin] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_27_2017 TBD] <br />
|-<br />
| March 6, 2017 || Becky Eastham || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_6_2017 TBD] <br />
|-<br />
| March 13, 2017 || Jim Brunner || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_13_2017 TBD] <br />
|-<br />
| March 20, 2017 || No Meeting - (UW Spring Break) || <br />
|-<br />
| March 27, 2017 || John Wiltshire-Gordon || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_27_2017 TBD] <br />
|-<br />
| April 3, 2017 || Will Mitchell || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017 TBD] <br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=High School Meetings=<br />
<br />
We are experimenting with holding some Math Circle meetings directly at local high schools. Our schedule for the fall is below. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2016<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| October 17, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~derman Daniel Erman] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016_.28JMM.29 What does math research look like?] ||<br />
|-<br />
| October 24, 2016 || 2:45pm West High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016_.28West.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| October 31, 2016 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016.28East.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| December 5, 2016 || 2:45pm East High || [http://www.math.wisc.edu/~andrews/ Uri Andrews] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28East.29 How to split an apartment] ||<br />
|-<br />
| December 5, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~pmwood Phillip Matchett Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28JMM.29 The game of Criss-Cross] ||<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| February 13, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~evaelduque Eva Elduque] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017_.28East.29 Pick's Theorem] ||<br />
|-<br />
| February 20, 2017 || 2:45pm JMM || [https://www.math.wisc.edu/~mmaguire2 Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017_.28JMM.29 Coloring Maps] ||<br />
|-<br />
| March 20, 2017 || 2:45pm East High || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| April 3rd, 2017 || 2:45pm JMM || [http://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017_.28JMM.29 Are we there yet?] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 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/lesson-plans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13366Madison Math Circle Abstracts2017-02-15T21:13:40Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
</center><br />
<br />
== February 13 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Dima Arinkin'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Solve it with colors'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
How many ways are there to place 32 dominoes on a 8x8 chessboard? (Dominoes cover exactly two squares, and should not overlap.) This is a very tough problem with a huge answer: 12,988,816. But suppose we want to only place 31 dominoes and leave two opposite corners empty. It turns out that the question is then almost trivial: such a placement is impossible. (Hint: The reason has to do with black and white squares on the board!)<br />
We will look at problems that can be solved by a clever coloring design. <br />
|}<br />
</center><br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!<br />
|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|}<br />
</center><br />
<br />
== April 3 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|}<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=13365Madison Math Circle2017-02-15T21:12:51Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<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.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <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/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.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_2hmb6vtDUfRonNb '''Math Circle Registration Form''']<br />
<br />
All of you 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 UW-Madison 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; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</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 UW-Madison 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 join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of three professors and three graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. 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: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:djbruce.jpg|[http://www.math.wisc.edu/~djbruce/ DJ 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 />
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 record-keeping, 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 2016 and Spring 2017=<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; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2016 <br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| <span style="color:red">August 6, 2016 <br> (Click Title for Time & Location.)</span> || [https://discovery.wisc.edu/programs/saturday-science Science Saturday] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#August_6_2016 Game Busters]<br />
|-<br />
| September 12, 2016 || [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_12_2016 Why do my earbuds keep getting entangled?]<br />
|-<br />
| September 19, 2016 || [http://www.math.wisc.edu/~djbruce/ DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_19_2016 Is Any Knot Not the Unkont? ] <br />
|-<br />
| September 26, 2016 || [http://mmaguire.weebly.com/ Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_26_2016 Coloring Maps] <br />
|-<br />
| October 3, 2016 || [http://www.math.wisc.edu/~zcharles/ Zach Charles] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_3_2016 1 + 1 = 10, or How does my smartphone do anything?] <br />
|-<br />
| October 10, 2016 || [http://www.math.wisc.edu/~jkrush/ Keith Rush] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_10_2016 Randomness, determinism and approximation: a historical question] <br />
|-<br />
| October 17, 2016 || [http://www.math.wisc.edu/~pmwood/ Phillip Matchett-Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016 The game of Criss-Cross]<br />
|-<br />
| October 24, 2016 || Ethan Biehl || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016 A Chocolate Bar for Every Real Number] <br />
|-<br />
| October 31, 2016 || No Meeting || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016 Enjoy Halloween!] <br />
|-<br />
| November 7, 2016 || [https://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_7_2016 Are we there yet?] <br />
|-<br />
| November 14, 2016 || [http://www.math.wisc.edu/~micky/ Micky Soule Steinberg] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_14_2016 Circles and Triangles] <br />
|-<br />
| November 21, 2016 || [https://www.math.wisc.edu/~valko/ Benedek Valko] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_21_2016 Fun with hats] <br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
|January 30, 2017 || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#January_30_2017 The Josephus Problem] <br />
|-<br />
| February 6, 2017 || Cullen McDonald || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_6_2017 Building a 4-dimensional house] <br />
|-<br />
| February 13, 2017 || Dima Arinkin || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017 Solve it with colors] <br />
|-<br />
| February 20, 2017 || Reese Johnston || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017 TBD] <br />
|-<br />
| February 27, 2017 || Jim Brunner || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_27_2017 TBD] <br />
|-<br />
| March 6, 2017 || Becky Eastham || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_6_2017 TBD] <br />
|-<br />
| March 13, 2017 || [https://www.math.wisc.edu/~jessica/ Jessica Lin] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_13_2017 TBD] <br />
|-<br />
| March 20, 2017 || No Meeting - (UW Spring Break) || <br />
|-<br />
| March 27, 2017 || John Wiltshire-Gordon || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_27_2017 TBD] <br />
|-<br />
| April 3, 2017 || Will Mitchell || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017 TBD] <br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=High School Meetings=<br />
<br />
We are experimenting with holding some Math Circle meetings directly at local high schools. Our schedule for the fall is below. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2016<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| October 17, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~derman Daniel Erman] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016_.28JMM.29 What does math research look like?] ||<br />
|-<br />
| October 24, 2016 || 2:45pm West High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016_.28West.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| October 31, 2016 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016.28East.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| December 5, 2016 || 2:45pm East High || [http://www.math.wisc.edu/~andrews/ Uri Andrews] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28East.29 How to split an apartment] ||<br />
|-<br />
| December 5, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~pmwood Phillip Matchett Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28JMM.29 The game of Criss-Cross] ||<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| February 13, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~evaelduque Eva Elduque] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017_.28East.29 Pick's Theorem] ||<br />
|-<br />
| February 20, 2017 || 2:45pm JMM || [https://www.math.wisc.edu/~mmaguire2 Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017_.28JMM.29 Coloring Maps] ||<br />
|-<br />
| March 20, 2017 || 2:45pm East High || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| April 3rd, 2017 || 2:45pm JMM || Polly Yu || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017_.28JMM.29 Are we there yet?] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 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/lesson-plans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=13364Graduate Algebraic Geometry Seminar2017-02-15T21:04:34Z<p>Djbruce: /* Spring 2017 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:40pm<br />
<br />
'''Where:'''Van Vleck B321 (Spring 2017)<br />
[[Image:cat.jpg|thumb|220px| | 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 in-depth.<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 />
* D-modules 101: basics of D-modules, equivalence between left and right D-modules, pullbacks, pushforwards, maybe the Gauss-Manin Connection. Claude Sabbah's introduction to the subject could be a good place to start.<br />
<br />
* Sheaf operations on D-modules (the point is that then you can get a Fourier-Mukai transform between certain O-modules and certain D-modules, 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 semi-orthogonal 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 (F-regularity, strong F-regularity, F-purity, 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, Brill-Noether 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 />
* ''Cayley-Bacharach Formulas'' - Qingchun Ren, Jürgen Richter-Gebert, 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 Gromov-Witten 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 A-infinity algebras and the derived category of a Calabi-Yau 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; font-size: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"|[[Graduate Algebraic Geometry Seminar#January 25 | Hodge to de Rham, part one]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 1<br />
| bgcolor="#C6D46E"| Nathan Clement<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 1 | Hodge to de Rham, part two]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 8 <br />
| bgcolor="#C6D46E"| Dima Arinkin<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 8 | Motivated introduction to geometric Langlands]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 15<br />
| bgcolor="#C6D46E"| No Talk<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 15 | We Failed, We All Failed]] <br />
|-<br />
| bgcolor="#E0E0E0"| February 22<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 22 | TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 1<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 1 | TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 8<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 8| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 15<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 15| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 22<br />
| bgcolor="#C6D46E"| Spring Break<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 22 | No Seminar. ]] <br />
|-<br />
| bgcolor="#E0E0E0"| March 29<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#March 29| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 5<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"| [[Graduate Algebraic Geometry Seminar#April 5| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 12<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 12| TBD]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 19<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 19| TBD ]] <br />
|-<br />
| bgcolor="#E0E0E0"| April 26<br />
| bgcolor="#C6D46E"| TBD<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 26| TBD ]] <br />
|}<br />
</center><br />
<br />
== January 25 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== February 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 8 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 15 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== March 22 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
== April 5 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: TBD<br />
|} <br />
</center><br />
<br />
<br />
== April 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size: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; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBA'''<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/~djbruce DJ 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>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=13354Madison Math Circle2017-02-14T14:41:12Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<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.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <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/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.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_2hmb6vtDUfRonNb '''Math Circle Registration Form''']<br />
<br />
All of you 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 UW-Madison 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; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</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 UW-Madison 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 join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of three professors and three graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. 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: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:djbruce.jpg|[http://www.math.wisc.edu/~djbruce/ DJ 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 />
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 record-keeping, 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 2016 and Spring 2017=<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; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2016 <br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| <span style="color:red">August 6, 2016 <br> (Click Title for Time & Location.)</span> || [https://discovery.wisc.edu/programs/saturday-science Science Saturday] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#August_6_2016 Game Busters]<br />
|-<br />
| September 12, 2016 || [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_12_2016 Why do my earbuds keep getting entangled?]<br />
|-<br />
| September 19, 2016 || [http://www.math.wisc.edu/~djbruce/ DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_19_2016 Is Any Knot Not the Unkont? ] <br />
|-<br />
| September 26, 2016 || [http://mmaguire.weebly.com/ Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_26_2016 Coloring Maps] <br />
|-<br />
| October 3, 2016 || [http://www.math.wisc.edu/~zcharles/ Zach Charles] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_3_2016 1 + 1 = 10, or How does my smartphone do anything?] <br />
|-<br />
| October 10, 2016 || [http://www.math.wisc.edu/~jkrush/ Keith Rush] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_10_2016 Randomness, determinism and approximation: a historical question] <br />
|-<br />
| October 17, 2016 || [http://www.math.wisc.edu/~pmwood/ Phillip Matchett-Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016 The game of Criss-Cross]<br />
|-<br />
| October 24, 2016 || Ethan Biehl || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016 A Chocolate Bar for Every Real Number] <br />
|-<br />
| October 31, 2016 || No Meeting || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016 Enjoy Halloween!] <br />
|-<br />
| November 7, 2016 || [https://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_7_2016 Are we there yet?] <br />
|-<br />
| November 14, 2016 || [http://www.math.wisc.edu/~micky/ Micky Soule Steinberg] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_14_2016 Circles and Triangles] <br />
|-<br />
| November 21, 2016 || [https://www.math.wisc.edu/~valko/ Benedek Valko] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_21_2016 Fun with hats] <br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
|January 30, 2017 || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#January_30_2017 The Josephus Problem] <br />
|-<br />
| February 6, 2017 || Cullen McDonald || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_6_2017 Building a 4-dimensional house] <br />
|-<br />
| February 13, 2017 || Dima Arinkin || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017 Solve it with colors] <br />
|-<br />
| February 20, 2017 || Reese Johnston || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017 TBD] <br />
|-<br />
| February 27, 2017 || Jim Brunner || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_27_2017 TBD] <br />
|-<br />
| March 6, 2017 || Becky Eastham || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_6_2017 TBD] <br />
|-<br />
| March 13, 2017 || [https://www.math.wisc.edu/~jessica/ Jessica Lin] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_13_2017 TBD] <br />
|-<br />
| March 20, 2017 || No Meeting - (UW Spring Break) || <br />
|-<br />
| March 27, 2017 || John Wiltshire-Gordon || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_27_2017 TBD] <br />
|-<br />
| April 3, 2017 || Will Mitchell || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017 TBD] <br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=High School Meetings=<br />
<br />
We are experimenting with holding some Math Circle meetings directly at local high schools. Our schedule for the fall is below. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2016<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| October 17, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~derman Daniel Erman] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016_.28JMM.29 What does math research look like?] ||<br />
|-<br />
| October 24, 2016 || 2:45pm West High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016_.28West.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| October 31, 2016 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016.28East.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| December 5, 2016 || 2:45pm East High || [http://www.math.wisc.edu/~andrews/ Uri Andrews] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28East.29 How to split an apartment] ||<br />
|-<br />
| December 5, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~pmwood Phillip Matchett Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28JMM.29 The game of Criss-Cross] ||<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| February 13, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~evaelduque Eva Elduque] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017_.28East.29 Pick's Theorem] ||<br />
|-<br />
| February 20, 2017 || 2:45pm JMM || [https://www.math.wisc.edu/~mmaguire2 Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017_.28JMM.29 Coloring Maps] ||<br />
|-<br />
| March 20, 2017 || 2:45pm East High || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| April 3rd, 2017 || 2:45pm JMM || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 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/lesson-plans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=13353Madison Math Circle2017-02-14T14:40:48Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<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.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <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/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.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_2hmb6vtDUfRonNb '''Math Circle Registration Form''']<br />
<br />
All of you 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 UW-Madison 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; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</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 UW-Madison 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 join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of three professors and three graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. 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: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:djbruce.jpg|[http://www.math.wisc.edu/~djbruce/ DJ 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 />
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 record-keeping, 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 2016 and Spring 2017=<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; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2016 <br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| <span style="color:red">August 6, 2016 <br> (Click Title for Time & Location.)</span> || [https://discovery.wisc.edu/programs/saturday-science Science Saturday] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#August_6_2016 Game Busters]<br />
|-<br />
| September 12, 2016 || [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_12_2016 Why do my earbuds keep getting entangled?]<br />
|-<br />
| September 19, 2016 || [http://www.math.wisc.edu/~djbruce/ DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_19_2016 Is Any Knot Not the Unkont? ] <br />
|-<br />
| September 26, 2016 || [http://mmaguire.weebly.com/ Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_26_2016 Coloring Maps] <br />
|-<br />
| October 3, 2016 || [http://www.math.wisc.edu/~zcharles/ Zach Charles] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_3_2016 1 + 1 = 10, or How does my smartphone do anything?] <br />
|-<br />
| October 10, 2016 || [http://www.math.wisc.edu/~jkrush/ Keith Rush] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_10_2016 Randomness, determinism and approximation: a historical question] <br />
|-<br />
| October 17, 2016 || [http://www.math.wisc.edu/~pmwood/ Phillip Matchett-Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016 The game of Criss-Cross]<br />
|-<br />
| October 24, 2016 || Ethan Biehl || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016 A Chocolate Bar for Every Real Number] <br />
|-<br />
| October 31, 2016 || No Meeting || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016 Enjoy Halloween!] <br />
|-<br />
| November 7, 2016 || [https://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_7_2016 Are we there yet?] <br />
|-<br />
| November 14, 2016 || [http://www.math.wisc.edu/~micky/ Micky Soule Steinberg] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_14_2016 Circles and Triangles] <br />
|-<br />
| November 21, 2016 || [https://www.math.wisc.edu/~valko/ Benedek Valko] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_21_2016 Fun with hats] <br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
|January 30, 2017 || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#January_30_2017 The Josephus Problem] <br />
|-<br />
| February 6, 2017 || Cullen McDonald || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_6_2017 Building a 4-dimensional house] <br />
|-<br />
| February 13, 2017 || Dima Arinkin || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017 Solve it with colors] <br />
|-<br />
| February 20, 2017 || Reese Johnston || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017 TBD] <br />
|-<br />
| February 27, 2017 || Jim Brunner || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_27_2017 TBD] <br />
|-<br />
| March 6, 2017 || Becky Eastham || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_6_2017 TBD] <br />
|-<br />
| March 13, 2017 || [https://www.math.wisc.edu/~jessica/ Jessica Lin] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_13_2017 TBD] <br />
|-<br />
| March 20, 2017 || No Meeting - (UW Spring Break) || <br />
|-<br />
| March 27, 2017 || John Wiltshire-Gordon || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_27_2017 TBD] <br />
|-<br />
| April 3, 2017 || Will Mitchell || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017 TBD] <br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=High School Meetings=<br />
<br />
We are experimenting with holding some Math Circle meetings directly at local high schools. Our schedule for the fall is below. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2016<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| October 17, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~derman Daniel Erman] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016_.28JMM.29 What does math research look like?] ||<br />
|-<br />
| October 24, 2016 || 2:45pm West High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016_.28West.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| October 31, 2016 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016.28East.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| December 5, 2016 || 2:45pm East High || [https://www.math.wisc.edu/~andrews/ Uri Andrews] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28East.29 How to split an apartment] ||<br />
|-<br />
| December 5, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~pmwood Phillip Matchett Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28JMM.29 The game of Criss-Cross] ||<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| February 13, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~evaelduque Eva Elduque] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017_.28East.29 Pick's Theorem] ||<br />
|-<br />
| February 20, 2017 || 2:45pm JMM || [https://www.math.wisc.edu/~mmaguire2 Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017_.28JMM.29 Coloring Maps] ||<br />
|-<br />
| March 20, 2017 || 2:45pm East High || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| April 3rd, 2017 || 2:45pm JMM || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 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/lesson-plans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=13352Madison Math Circle2017-02-14T14:39:47Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<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.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <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/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.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_2hmb6vtDUfRonNb '''Math Circle Registration Form''']<br />
<br />
All of you 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 UW-Madison 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; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</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 UW-Madison 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 join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of three professors and three graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. 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: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:djbruce.jpg|[http://www.math.wisc.edu/~djbruce/ DJ 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 />
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 record-keeping, 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 2016 and Spring 2017=<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; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2016 <br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| <span style="color:red">August 6, 2016 <br> (Click Title for Time & Location.)</span> || [https://discovery.wisc.edu/programs/saturday-science Science Saturday] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#August_6_2016 Game Busters]<br />
|-<br />
| September 12, 2016 || [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_12_2016 Why do my earbuds keep getting entangled?]<br />
|-<br />
| September 19, 2016 || [http://www.math.wisc.edu/~djbruce/ DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_19_2016 Is Any Knot Not the Unkont? ] <br />
|-<br />
| September 26, 2016 || [http://mmaguire.weebly.com/ Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_26_2016 Coloring Maps] <br />
|-<br />
| October 3, 2016 || [http://www.math.wisc.edu/~zcharles/ Zach Charles] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_3_2016 1 + 1 = 10, or How does my smartphone do anything?] <br />
|-<br />
| October 10, 2016 || [http://www.math.wisc.edu/~jkrush/ Keith Rush] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_10_2016 Randomness, determinism and approximation: a historical question] <br />
|-<br />
| October 17, 2016 || [http://www.math.wisc.edu/~pmwood/ Phillip Matchett-Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016 The game of Criss-Cross]<br />
|-<br />
| October 24, 2016 || Ethan Biehl || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016 A Chocolate Bar for Every Real Number] <br />
|-<br />
| October 31, 2016 || No Meeting || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016 Enjoy Halloween!] <br />
|-<br />
| November 7, 2016 || [https://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_7_2016 Are we there yet?] <br />
|-<br />
| November 14, 2016 || [http://www.math.wisc.edu/~micky/ Micky Soule Steinberg] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_14_2016 Circles and Triangles] <br />
|-<br />
| November 21, 2016 || [https://www.math.wisc.edu/~valko/ Benedek Valko] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_21_2016 Fun with hats] <br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
|January 30, 2017 || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#January_30_2017 The Josephus Problem] <br />
|-<br />
| February 6, 2017 || Cullen McDonald || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_6_2017 Building a 4-dimensional house] <br />
|-<br />
| February 13, 2017 || Dima Arinkin || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017 Solve it with colors] <br />
|-<br />
| February 20, 2017 || Reese Johnston || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017 TBD] <br />
|-<br />
| February 27, 2017 || Jim Brunner || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_27_2017 TBD] <br />
|-<br />
| March 6, 2017 || Becky Eastham || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_6_2017 TBD] <br />
|-<br />
| March 13, 2017 || [https://www.math.wisc.edu/~jessica/ Jessica Lin] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_13_2017 TBD] <br />
|-<br />
| March 20, 2017 || No Meeting - (UW Spring Break) || <br />
|-<br />
| March 27, 2017 || John Wiltshire-Gordon || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_27_2017 TBD] <br />
|-<br />
| April 3, 2017 || Will Mitchell || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017 TBD] <br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=High School Meetings=<br />
<br />
We are experimenting with holding some Math Circle meetings directly at local high schools. Our schedule for the fall is below. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2016<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| October 17, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~derman Daniel Erman] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016_.28JMM.29 What does math research look like?] ||<br />
|-<br />
| October 24, 2016 || 2:45pm West High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016_.28West.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| October 31, 2016 || 2:45pm East High || [https://www.math.wisc.edu/~djbruce DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016.28East.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| December 5, 2016 || 2:45pm East High || [https://www.math.wisc.edu/~andrews Uri Andrews] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28East.29 How to split an apartment] ||<br />
|-<br />
| December 5, 2016 || 2:45pm JMM || [https://www.math.wisc.edu/~pmwood Phillip Matchett Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28JMM.29 The game of Criss-Cross] ||<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| February 13, 2017 || 2:45pm East High || [https://www.math.wisc.edu/~evaelduque Eva Elduque] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017_.28East.29 Pick's Theorem] ||<br />
|-<br />
| February 20, 2017 || 2:45pm JMM || [https://www.math.wisc.edu/~mmaguire2 Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017_.28JMM.29 Coloring Maps] ||<br />
|-<br />
| March 20, 2017 || 2:45pm East High || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| April 3rd, 2017 || 2:45pm JMM || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 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/lesson-plans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=13330Madison Math Circle2017-02-08T21:18:31Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<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.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <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/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.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_2hmb6vtDUfRonNb '''Math Circle Registration Form''']<br />
<br />
All of you 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 UW-Madison 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; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</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 UW-Madison 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 join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of three professors and three graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. 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: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:djbruce.jpg|[http://www.math.wisc.edu/~djbruce/ DJ 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 />
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 record-keeping, 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 2016 and Spring 2017=<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; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2016 <br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| <span style="color:red">August 6, 2016 <br> (Click Title for Time & Location.)</span> || [https://discovery.wisc.edu/programs/saturday-science Science Saturday] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#August_6_2016 Game Busters]<br />
|-<br />
| September 12, 2016 || [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_12_2016 Why do my earbuds keep getting entangled?]<br />
|-<br />
| September 19, 2016 || [http://www.math.wisc.edu/~djbruce/ DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_19_2016 Is Any Knot Not the Unkont? ] <br />
|-<br />
| September 26, 2016 || [http://mmaguire.weebly.com/ Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_26_2016 Coloring Maps] <br />
|-<br />
| October 3, 2016 || [http://www.math.wisc.edu/~zcharles/ Zach Charles] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_3_2016 1 + 1 = 10, or How does my smartphone do anything?] <br />
|-<br />
| October 10, 2016 || [http://www.math.wisc.edu/~jkrush/ Keith Rush] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_10_2016 Randomness, determinism and approximation: a historical question] <br />
|-<br />
| October 17, 2016 || [http://www.math.wisc.edu/~pmwood/ Phillip Matchett-Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016 The game of Criss-Cross]<br />
|-<br />
| October 24, 2016 || Ethan Biehl || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016 A Chocolate Bar for Every Real Number] <br />
|-<br />
| October 31, 2016 || No Meeting || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016 Enjoy Halloween!] <br />
|-<br />
| November 7, 2016 || [https://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_7_2016 Are we there yet?] <br />
|-<br />
| November 14, 2016 || [http://www.math.wisc.edu/~micky/ Micky Soule Steinberg] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_14_2016 Circles and Triangles] <br />
|-<br />
| November 21, 2016 || [https://www.math.wisc.edu/~valko/ Benedek Valko] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_21_2016 Fun with hats] <br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
|January 30, 2017 || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#January_30_2017 The Josephus Problem] <br />
|-<br />
| February 6, 2017 || Cullen McDonald || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_6_2017 Building a 4-dimensional house] <br />
|-<br />
| February 13, 2017 || Dima Arinkin || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017 TBD] <br />
|-<br />
| February 20, 2017 || Reese Johnston || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017 TBD] <br />
|-<br />
| February 27, 2017 || Jim Brunner || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_27_2017 TBD] <br />
|-<br />
| March 6, 2017 || Becky Eastham || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_6_2017 TBD] <br />
|-<br />
| March 13, 2017 || [https://www.math.wisc.edu/~jessica/ Jessica Lin] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_13_2017 TBD] <br />
|-<br />
| March 20, 2017 || No Meeting - (UW Spring Break) || <br />
|-<br />
| March 27, 2017 || John Wiltshire-Gordon || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_27_2017 TBD] <br />
|-<br />
| April 3, 2017 || Will Mitchell || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017 TBD] <br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=High School Meetings=<br />
<br />
We are experimenting with holding some Math Circle meetings directly at local high schools. Our schedule for the fall is below. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2016<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| October 17, 2016 || 2:45pm JMM || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016_.28JMM.29 What does math research look like?] ||<br />
|-<br />
| October 24, 2016 || 2:45pm West High || DJ Bruce || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016_.28West.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| October 31, 2016 || 2:45pm East High || DJ Bruce || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016.28East.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| December 5, 2016 || 2:45pm East High || Uri Andrews || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28East.29 How to split an apartment] ||<br />
|-<br />
| December 5, 2016 || 2:45pm JMM || Phillip Matchett Wood || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28JMM.29 The game of Criss-Cross] ||<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| February 13, 2017 || 2:45pm East High || Eva Elduque || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017_.28East.29 Pick's Theorem] ||<br />
|-<br />
| February 20, 2017 || 2:45pm JMM || Megan Maguire || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017_.28JMM.29 Coloring Maps] ||<br />
|-<br />
| March 20, 2017 || 2:45pm East High || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| April 3rd, 2017 || 2:45pm JMM || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 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/lesson-plans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle&diff=13329Madison Math Circle2017-02-08T21:18:14Z<p>Djbruce: /* High School Meetings */</p>
<hr />
<div>[[Image:logo.png|right|440px]]<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.jpg|500px]] [[Image: MathCircle_4.jpg|500px]] <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/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.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_2hmb6vtDUfRonNb '''Math Circle Registration Form''']<br />
<br />
All of you 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 UW-Madison 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; margin-left:auto; margin-right:auto;"><br />
[[File: Helencwhitemap.png|400px]]</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 UW-Madison 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 join-mathcircle@lists.wisc.edu<br />
<br />
==Contact the organizers==<br />
The Madison Math Circle is organized by a group of three professors and three graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. 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: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:djbruce.jpg|[http://www.math.wisc.edu/~djbruce/ DJ 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 />
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 record-keeping, 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 2016 and Spring 2017=<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; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Fall 2016 <br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
| <span style="color:red">August 6, 2016 <br> (Click Title for Time & Location.)</span> || [https://discovery.wisc.edu/programs/saturday-science Science Saturday] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#August_6_2016 Game Busters]<br />
|-<br />
| September 12, 2016 || [http://www.math.wisc.edu/~jeanluc/ Jean-Luc Thiffeault] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_12_2016 Why do my earbuds keep getting entangled?]<br />
|-<br />
| September 19, 2016 || [http://www.math.wisc.edu/~djbruce/ DJ Bruce] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_19_2016 Is Any Knot Not the Unkont? ] <br />
|-<br />
| September 26, 2016 || [http://mmaguire.weebly.com/ Megan Maguire] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#September_26_2016 Coloring Maps] <br />
|-<br />
| October 3, 2016 || [http://www.math.wisc.edu/~zcharles/ Zach Charles] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_3_2016 1 + 1 = 10, or How does my smartphone do anything?] <br />
|-<br />
| October 10, 2016 || [http://www.math.wisc.edu/~jkrush/ Keith Rush] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_10_2016 Randomness, determinism and approximation: a historical question] <br />
|-<br />
| October 17, 2016 || [http://www.math.wisc.edu/~pmwood/ Phillip Matchett-Wood] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016 The game of Criss-Cross]<br />
|-<br />
| October 24, 2016 || Ethan Biehl || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016 A Chocolate Bar for Every Real Number] <br />
|-<br />
| October 31, 2016 || No Meeting || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016 Enjoy Halloween!] <br />
|-<br />
| November 7, 2016 || [https://www.math.wisc.edu/~pollyyu/ Polly Yu] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_7_2016 Are we there yet?] <br />
|-<br />
| November 14, 2016 || [http://www.math.wisc.edu/~micky/ Micky Soule Steinberg] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_14_2016 Circles and Triangles] <br />
|-<br />
| November 21, 2016 || [https://www.math.wisc.edu/~valko/ Benedek Valko] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#November_21_2016 Fun with hats] <br />
|-<br />
! colspan="3" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
! Date !! Speaker !! Topic<br />
|-<br />
|January 30, 2017 || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#January_30_2017 The Josephus Problem] <br />
|-<br />
| February 6, 2017 || Cullen McDonald || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_6_2017 Building a 4-dimensional house] <br />
|-<br />
| February 13, 2017 || Dima Arinkin || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017 TBD] <br />
|-<br />
| February 20, 2017 || Reese Johnston || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017 TBD] <br />
|-<br />
| February 27, 2017 || Jim Brunner || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_27_2017 TBD] <br />
|-<br />
| March 6, 2017 || Becky Eastham || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_6_2017 TBD] <br />
|-<br />
| March 13, 2017 || [https://www.math.wisc.edu/~jessica/ Jessica Lin] || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_13_2017 TBD] <br />
|-<br />
| March 20, 2017 || No Meeting - (UW Spring Break) || <br />
|-<br />
| March 27, 2017 || John Wiltshire-Gordon || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#March_27_2017 TBD] <br />
|-<br />
| April 3, 2017 || Will Mitchell || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#April_3_2017 TBD] <br />
|-<br />
|}<br />
<br />
</center><br />
<br />
=High School Meetings=<br />
<br />
We are experimenting with holding some Math Circle meetings directly at local high schools. Our schedule for the fall is below. If you are interesting in having us come to your high school, please contact us!<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Fall 2016<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| October 17, 2016 || 2:45pm JMM || Daniel Erman || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_17_2016_.28JMM.29 What does math research look like?] ||<br />
|-<br />
| October 24, 2016 || 2:45pm West High || DJ Bruce || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_24_2016_.28West.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| October 31, 2016 || 2:45pm East High || DJ Bruce || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#October_31_2016.28East.29 Shhh, This Message Is Secret] ||<br />
|-<br />
| December 5, 2016 || 2:45pm East High || Uri Andrews || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28East.29 How to split an apartment] ||<br />
|-<br />
| December 5, 2016 || 2:45pm JMM || Phillip Matchett Wood || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#December_5_2016_.28JMM.29 The game of Criss-Cross] ||<br />
|-<br />
! colspan="5" style="background: #e8b2b2;" align="center" | Spring 2017<br />
|-<br />
|-<br />
! Date !! Location !! Speaker !! Topic !! Link for more info<br />
|-<br />
| February 13, 2017 || 2:45pm East High || Eva Elduque || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_13_2017_.28East.29 Pick's Theorem] ||<br />
|-<br />
| February 20, 2017 || 2:45pm JMM || Megan Meguire || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts#February_20_2017_.28JMM.29 Coloring Maps] ||<br />
|-<br />
| March 20, 2017 || 2:45pm East High || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| April 3rd, 2017 || 2:45pm JMM || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
| TBD || TBD || TBD || [https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts TBD] ||<br />
|-<br />
|}<br />
</center><br />
<br />
=Useful Resources=<br />
==Annual Reports==<br />
[https://www.math.wisc.edu/wiki/images/Math_Circle_Newsletter.pdf 2013-2014 Annual Report]<br />
<br />
== Archived Abstracts ==<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 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/lesson-plans Sample Lesson Plans]<br />
<br />
[http://www.mathcircles.org/content/circle-box "Circle in a Box"]</div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13328Madison Math Circle Abstracts2017-02-08T21:16:34Z<p>Djbruce: </p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!<br />
|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|}<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13327Madison Math Circle Abstracts2017-02-08T21:16:02Z<p>Djbruce: </p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Ethan Beihl'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: A Chocolate Bar for Every Real Number'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
By chopping up rectangles into squares repeatedly we obtain so-called "slicing diagrams" that correspond to every number. These diagrams have some very cool properties, and show up all over mathematics (under the name "continued fractions," which name we will investigate). Some questions I may ask you: Which chocolate bars look like themselves? Which chocolate bars look like themselves, except bigger? Which chocolate bars are interesting? Why did you come to a math talk expecting real chocolate?<br />
|} <br />
</center><br />
<br />
== October 31 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''No Meeting This Week'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: N/A'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
Enjoy Halloween.<br />
|} <br />
</center><br />
<br />
== November 7 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Polly Yu'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Are we there yet?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
When you are told to clean your room, you have to first clean half of it; then half of what's left, and half of what's left, and so on. Seems like you will never be done! In fact, an ancient Greek philosopher, Zeno, used an argument like this to claim that it is impossible to move! Disclaimer: we are not saying that it's impossible to clean your room. What we will do is look at a special case of adding infinitely many numbers together, and use the resulting formula to calculate areas of fractals.<br />
|} <br />
</center><br />
<br />
== November 14 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Micky Soule Steinberg'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Circles and Triangles'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We’ll talk about the pythagorean theorem and areas of circles/triangles, and then use those tools to solve some cool problems!<br />
|} <br />
</center><br />
<br />
== November 21 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Benedek Valko'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Fun with hats'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
We will discuss various fun logic problems involving colors of hats. The participants will also have a chance to win some of the speaker’s leftover Halloween candy. <br />
|} <br />
</center><br />
<br />
<br />
== February 6 2017 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Cullen McDonald'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Building a 4-dimensional house'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
<br />
I think my dream home would be in the fourth dimension. I'd have a lot more room for activities. We will draw blueprints, build models, and measure how much more room we'll get by using mathematics to extend our understanding of 3 dimensions to 4 or beyond. <br />
|}<br />
<br />
= High School Meetings =<br />
== October 17 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Daniel Erman'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: What does math research look like?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Using a concrete problem in combinatorics, I will try to give a feel for what math research looks like. We’ll discuss the various aspects of research including: gathering data, making conjectures, proving special cases, and asking new questions.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 2016 (West) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or. <br />
<br />
|} <br />
</center><br />
<br />
== October 31 2016 (East)==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Shhh, This Message Is Secret'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
gur pbearefgbar bs gur zbqrea jbeyq eribyirf nebhaq orvat noyr gb rnfvyl pbzzhavpngr frpergf, jurgure gubfr frpergf or perqvg pneq ahzoref ba nznmba, grkg zrffntrf ba lbhe vcubar, be frpher tbireazrag nssnvef. va guvf gnyx jr jvyy rkcyber gur zngu haqrecvaavat bhe novyvgl gb qb guvf, naq frr whfg ubj fgheql gung pbearefgbar npghnyyl znl or.<br />
|} <br />
</center><br />
<br />
== December 5 2016 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Philip Matchett Wood'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: The game of Criss-Cross'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Some say that mathematics is the science of patterns, and patterns are everywhere. You can find some remarkable patterns just by drawing lines connecting dots, and that is just what we will do in the game of Criss-Cross! Bring your pencils and be ready to play.<br />
<br />
|} <br />
</center><br />
<br />
== December 5 2016 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: How to split an apartment'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
So you go off to college and after a year or two, you and some of your friends decide to get an apartment together. It'll be a lot of fun living with your best friends. Then move-in day comes, and you realize that everyone wants the room by the kitchen (for easy late-night snacking). You have 4 rooms and 4 people. Surely there must be some way to make everybody happy. People are willing to settle for their second-favorite room instead if maybe they pay a little less rent or do some less chores. How do you navigate this issue to make everybody happy? I'll share a way to do this based on a mathematical theorem which also explains the following fact: If you stir up a cup of hot chocolate, when the liquid has come to rest, some point in the liquid will end up in exactly the same place in the cup as before you stirred it.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 2017 (East) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Eva Elduque'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Pick's Theorem'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
In this talk, we will work to discover a beautiful formula that allows us to quickly and easily compute the area of a polygon whose vertices are points of a grid. We will prove that this formula works!|} <br />
</center><br />
<br />
== February 20 2017 (JMM) ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
</center></div>Djbrucehttps://www.math.wisc.edu/wiki/index.php?title=Madison_Math_Circle_Abstracts&diff=13312Madison Math Circle Abstracts2017-02-08T14:56:49Z<p>Djbruce: /* February 13 2017 (East) */</p>
<hr />
<div>[[Image:logo.png|right|440px|link=https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle]]<br />
<br />
== August 6 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Science Saturday'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Game Busters'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
The goal of our station will be to explore the mathematics related to the games: Set, Nim, and Chomp. We will have stations where individuals can drop by play a few games and explore these games for themselves. (We will have worksheets and volunteers providing guidance.) Additionally, anyone will be able to challenge our Master of Nim with fun prizes available for beating them. (Note: This is at a special time and location.)<br />
<ul><br />
<li> [https://www.math.wisc.edu/wiki/images/Chomp_Sol.pdf Solutions for Chomp] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Nim_sol.pdf Solutions for Nim] </li><br />
<li> [https://www.math.wisc.edu/wiki/images/Set_sol.pdf Solutions for Set].</li><br />
</ul><br />
|} <br />
</center><br />
<br />
== September 12 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Jean-Luc Thiffeault'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Why do my earbuds keep getting entangled?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
I'll discuss the mathematics of random entanglements. Why is it that<br />
it's so easy for wires to get entangled, but so hard for them to<br />
detangle?<br />
|} <br />
</center><br />
<br />
== September 19 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''DJ Bruce'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Is Any Knot Not the Unknot?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.<br />
|} <br />
</center><br />
<br />
== September 26 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Coloring Maps'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Have you ever noticed that in colored maps of the US bordering states are never the same color? That's because it would be super confusing! But how many different colors do we need in order to avoid this? Come find out and learn more cool things about coloring maps.<br />
|} <br />
</center><br />
<br />
== October 3 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Zach Charles'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: 1 + 1 = 10, or How does my smartphone do anything?'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
Computers are used to do all kinds of complex tasks, from playing videos to running internet browsers. Secretly, computers do everything through numbers and mathematics. Surprisingly, they do all of this with "bits", numbers that are only 0 or 1. We will talk about bits and how we use them to do the mathematics we're familiar with as humans. If we have enough time, we will discuss "addition chains" and how computers use them to speed up their computations.<br />
|} <br />
</center><br />
<br />
== October 10 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Keith Rush'''<br />
|-<br />
| bgcolor="#BDBDBD" align="center" | '''Title: Randomness, determinism and approximation: a historical question'''<br />
|-<br />
| bgcolor="#BDBDBD" | <br />
If you give me a function, can I find a simple function that approximates it well? This question played a central role in the development of mathematics. With a couple examples we will begin to investigate this for ourselves, and we'll touch on some interesting relationships to modeling random processes.<br />
<br />
|} <br />
</center><br />
<br />
== October 17 2016 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#e8b2b2" align="center&am