Difference between revisions of "Graduate Algebraic Geometry Seminar"

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'''
 
'''
'''When:''' Wednesdays 4:10pm
+
'''When:''' Wednesdays 4:25pm
  
'''Where:''' Van Vleck B215 (Fall 2018)
+
'''Where:''' Van Vleck B317
 
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]
 
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]
  
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'''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].
 
'''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].
 
'''
 
'''
 
== Organize the seminar! ==
 
 
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''
 
  
 
== Give a talk! ==
 
== Give a talk! ==
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.
+
We need volunteers to give talks this semester. If you're interested contact [mailto:cwcrowley@wisc.edu Colin] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.
 
 
 
 
  
 
== Being an audience member ==
 
== Being an audience member ==
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* DG Schemes.
 
* DG Schemes.
  
 
+
==Ed Dewey's Wish List Of Olde==__NOTOC__
==Ed Dewey's Wish List Of Olde==
 
  
 
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.
 
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.
Line 65: Line 58:
  
 
* 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)
 
* 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)
 
===Famous Theorems===
 
  
 
===Interesting Papers & Books===
 
===Interesting Papers & Books===
Line 109: Line 100:
 
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.
 
* ''The Gromov-Witten potential associated to a TCFT'' - Kevin J. Costello.
 
** 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.)
 
** 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.)
__NOTOC__
 
  
== Autumn 2018 ==
+
== Spring 2020 ==
  
 
<center>
 
<center>
Line 120: Line 110:
 
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''
 
| bgcolor="#BCD2EE" width="300" align="center"|'''Title (click to see abstract)'''
 
|-
 
|-
| bgcolor="#E0E0E0"| September 12
+
| bgcolor="#E0E0E0"| January 29
| bgcolor="#C6D46E"| Moisés Herradón Cueto
+
| bgcolor="#C6D46E"| Colin Crowley
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#January 29| Lefschetz hyperplane section theorem via Morse theory]]
 
|-
 
|-
| bgcolor="#E0E0E0"| September 19
+
| bgcolor="#E0E0E0"| February 5
| bgcolor="#C6D46E"| Caitlyn Booms
+
| bgcolor="#C6D46E"| Asvin Gothandaraman
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 5| An Introduction to Unirationality]]
 
|-
 
|-
| bgcolor="#E0E0E0"| September 26
+
| bgcolor="#E0E0E0"| February 12
 
| bgcolor="#C6D46E"| Qiao He
 
| bgcolor="#C6D46E"| Qiao He
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 12| Title]]
 
|-
 
|-
| bgcolor="#E0E0E0"| October 3
+
| bgcolor="#E0E0E0"| February 19
| bgcolor="#C6D46E"| Wanlin Li
+
| bgcolor="#C6D46E"| Dima Arinkin
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 19| Blowing down, blowing up: surface geometry]]
 
|-
 
|-
| bgcolor="#E0E0E0"| October 10
+
| bgcolor="#E0E0E0"| February 26
| bgcolor="#C6D46E"| Ewan Dalby
+
| bgcolor="#C6D46E"| Connor Simpson
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 26| Intro to toric varieties]]
 
|-
 
|-
| bgcolor="#E0E0E0"| October 17
+
| bgcolor="#E0E0E0"| March 4
| bgcolor="#C6D46E"| Johnnie Han
+
| bgcolor="#C6D46E"| Peter
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 4| Title]]
 
|-
 
|-
| bgcolor="#E0E0E0"| October 24
+
| bgcolor="#E0E0E0"| March 11
| bgcolor="#C6D46E"| Solly Parenti
+
| bgcolor="#C6D46E"| Caitlyn Booms
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 11| Title]]
|-
 
| bgcolor="#E0E0E0"| October 31
 
| bgcolor="#C6D46E"| Brandon Boggess
 
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]
 
 
|-
 
|-
| bgcolor="#E0E0E0"| November 7
+
| bgcolor="#E0E0E0"| March 25
| bgcolor="#C6D46E"| Vladimir Sotirov
+
| bgcolor="#C6D46E"| Steven He
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| Morita Duality and Local Duality]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 25| Title]]
 
|-
 
|-
| bgcolor="#E0E0E0"| November 14
+
| bgcolor="#E0E0E0"| April 1
| bgcolor="#C6D46E"| David Wagner
+
| bgcolor="#C6D46E"| Vlad Sotirov
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| Homological Projective Duality]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 1| Title]]
 
|-
 
|-
| bgcolor="#E0E0E0"| November 21
+
| bgcolor="#E0E0E0"| April 8
| bgcolor="#C6D46E"| A turkey/Smallpox
+
| bgcolor="#C6D46E"| Maya Banks
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 8| Title]]
 
|-
 
|-
| bgcolor="#E0E0E0"| November 28
+
| bgcolor="#E0E0E0"| April 15
| bgcolor="#C6D46E"| Asvin Gothandaraman
+
| bgcolor="#C6D46E"| Alex Mine
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| Deformation Theory]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 15| Title]]
 
|-
 
|-
| bgcolor="#E0E0E0"| December 5
+
| bgcolor="#E0E0E0"| April 22
| bgcolor="#C6D46E"| Soumya Sankar
+
| bgcolor="#C6D46E"| Ruofan
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| One Step Closer to <math>B_{cris}</math>]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 22| Title]]
 
|-
 
|-
| bgcolor="#E0E0E0"| December 12
+
| bgcolor="#E0E0E0"| April 29
| bgcolor="#C6D46E"| Sun Woo Park
+
| bgcolor="#C6D46E"| John Cobb
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| A Survey of Newton Polygons]]
+
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 29| Title]]
 
|}
 
|}
 
</center>
 
</center>
  
== September 12 ==
+
== January 29 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: Hodge Theory: One hour closer to understanding what it's about
+
| bgcolor="#BCD2EE"  align="center" | Title: Lefschetz hyperplane section theorem via Morse theory
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract: Morse theory allows you to learn about the topology of a manifold by studying the critical points of a nice function on the manifold. This perspective produces a nice proof of the theorem in the title, which concerns the homology of smooth projective varieties over C. I'll explain what the theorem says, say something about what Morse theory is and why it's related, and then finish with a neat example. I'm aiming to make this understandable to someone who's taken algebraic geometry 1 and topology 1.
Abstract:  
 
 
 
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== September 19 ==
+
== February 5 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman '''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: Linear Resolutions of Edge Ideals
+
| bgcolor="#BCD2EE"  align="center" | Title: An introduction to unirationality
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract: I will introduce the notion of unirationality and show that cubic hypersurfaces are unirational (following Kollar). If time permits, I will also show that unirational varieties are simply connected.  
Abstract:  
 
 
 
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== September 26 ==
+
== February 12 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
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| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: An Elementary Introduction to Geometric Langlands
+
| bgcolor="#BCD2EE"  align="center" | Title:  
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract:  
Abstract:  
 
 
 
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== October 3 ==
+
== February 19 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: Gonality of Curves and More
+
| bgcolor="#BCD2EE"  align="center" | Title: Blowing down, blowing up: surface geometry
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract:A big question in algebraic geometry is how much one can change a variety without affecting it `generically'. More precisely, if two varieties are birational, how far can they be from being isomorphic?
Abstract:  
 
  
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves.  
+
The question is trivial for (smooth projective) curves: they are birational if and only if they are isomorphic. In higher dimension, the
|}                                                                       
+
situation is much more interesting. The most fundamental operation are the `blowup', which is a kind of alteration of a variety within its birational isomorphism class, and its opposite, the blowdown.
</center>
 
 
 
== October 10 ==
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title: A Gentle introduction to Grothendiecks Galois theory
 
|-
 
| bgcolor="#BCD2EE"  | 
 
Abstract:
 
  
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.
+
In my talk, I will introduce blowups and discuss their properties. Then (time permitting) I would like to look deeper at the case
 +
of surfaces, where the combination of blowups and intersection theory provides a complete and beautiful picture. (If we do get to this point, I won't assume any knowledge of intersection theory: to an extent, this talk is my excuse to introduce it.)
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== October 17 ==
+
== February 26 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: Schubert Calculus
+
| bgcolor="#BCD2EE"  align="center" | Title: Intro to Toric Varieties
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract: A brief introduction to toric varieties: how to build them, formulas for computing topological data, toric blow-ups, and more.
Abstract:  
 
 
 
In this talk, we’ll go back to 19th-century Europe, when enumerative geometric questions like “how many lines intersect a quadric” or “how many lines lie on a cubic surface” were answered without even knowing the intersection pairing existed! We’ll go through the methods of Schubert calculus with examples and talk briefly about Steiner’s conics problem, when a famous mathematician was actually proven completely wrong.
 
 
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== October 24 ==
+
== March 4 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Peter'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: Quadratic Polynomials
+
| bgcolor="#BCD2EE"  align="center" | Title:  
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract:  
Abstract:  
 
 
 
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== October 31 ==
+
== March 11 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Brandon Boggess'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: How to Parameterize Elliptic Curves and Influence People
+
| bgcolor="#BCD2EE"  align="center" | Title:  
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract:  
Abstract:  
 
 
 
A classical guide to classifying curves for the geometrically minded grad student. I will assume basically zero AG background.
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== November 7 ==
+
== March 25 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vladimir Sotirov'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Steven He'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: Morita duality and local duality
+
| bgcolor="#BCD2EE"  align="center" | Title:  
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract:  
Abstract:
 
 
 
I will explain what it means for a ring to admit a dualizing module and how to construct such for nice local rings.
 
 
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== November 14 ==
+
== April 1 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''David Wagner'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vlad Sotirov'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: Homological Projective Duality
+
| bgcolor="#BCD2EE"  align="center" | Title:  
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract:  
Abstract:  
 
 
 
I will introduce the derived category with the goal of undestanding Kuznetsov's HPD, a mysterious phenomenon which has produced a great number of examples and theorems in AG. We will give a demonstration of the duality in the case of an intersection of quadrics.
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== November 21 ==
+
== April 8 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Maya Banks'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: TBD
+
| bgcolor="#BCD2EE"  align="center" | Title:  
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract:  
Abstract:  
 
 
 
TBD
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== November 28 ==
+
== April 15 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin G'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Mine'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: Deformation Theory
+
| bgcolor="#BCD2EE"  align="center" | Title:  
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract:  
Abstract:  
 
 
 
I will explain what deformation theory is and how to use it by doing a few examples.
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== November 7 ==
+
== April 22 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''TBD'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ruofan'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: TBD
+
| bgcolor="#BCD2EE"  align="center" | Title:  
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract:  
Abstract:  
 
 
 
TBD
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== December 5 ==
+
== April 29 ==
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''
+
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Cobb'''
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: One Step Closet to <math>B_{cris}</math>
+
| bgcolor="#BCD2EE"  align="center" | Title:  
 
|-
 
|-
| bgcolor="#BCD2EE"  |  
+
| bgcolor="#BCD2EE"  | Abstract:  
Abstract: I will talk about various comparison theorems in <math>p</math>-adic cohomology, and time permitting, describe the crystalline side of things in greater detail.
 
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
  
== December 12 ==
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Sun Woo Park'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title: A Survey of Newton Polygons
 
|-
 
| bgcolor="#BCD2EE"  | 
 
Abstract: I will give a survey on how understanding newton polygons can be useful in solving many different problems in algebraic geometry: from the proof of p-adic Weierstrass Formula to the re-formulization of Tate's Algorithm for elliptic curves. (Since I will focus on providing various applications of newton polygons, I will not be able to present rigorous proofs to most of the statements I will make in this talk.)
 
  
|}                                                                       
+
== Organizers' Contact Info ==
</center>
 
  
== Organizers' Contact Info ==
+
[https://sites.google.com/view/colincrowley/home Colin Crowley]
  
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]
+
[http://www.math.wisc.edu/~drwagner/ David Wagner]
  
 
== Past Semesters ==
 
== Past Semesters ==
 +
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2019 Fall 2019]
 +
 +
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2019 Spring 2019]
 +
 +
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]
 +
 
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]
 
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]
  

Revision as of 23:22, 24 February 2020

When: Wednesdays 4:25pm

Where: Van Vleck B317

Lizzie the OFFICIAL mascot of GAGS!!

Who: All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.

Why: The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying in-depth. Regardless the goal of GAGS is to provide a supportive and inclusive place for all to learn more about algebraic geometry and commutative algebra.

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 here.

Give a talk!

We need volunteers to give talks this semester. If you're interested contact Colin or David, or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.

Being an audience member

The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:

  • Do Not Speak For/Over the Speaker:
  • Ask Questions Appropriately:

The List of Topics that we Made February 2018

On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:

Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.

  • Schubert Calculus, aka how many lines intersect four given lines in three-dimensional space? The answer to this question is prettiest when you think about it as a problem of intersecting subvarieties in the Grassmanian. What is the Grassmanian, you say? That's probably a talk we should have every year, so you should give it!
  • Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.
  • Katz and Mazur explanation of what a modular form is. What is it?
  • Kindergarten moduli of curves.
  • What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?
  • Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)
  • Hodge theory for babies
  • What is a Néron model?
  • What and why is a dessin d'enfants?
  • DG Schemes.

Ed Dewey's Wish List Of Olde

Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.

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.

Specifically Vague Topics

  • 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.
  • 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)

Interesting Papers & Books

  • Symplectic structure of the moduli space of sheaves on an abelian or K3 surface - Shigeru Mukai.
  • Residues and Duality - Robin Hatshorne.
    • 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 ;).)
  • Coherent sheaves on P^n and problems in linear algebra - A. A. Beilinson.
    • 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.)
  • Frobenius splitting and cohomology vanishing for Schubert varieties - V.B. Mehta and A. Ramanathan.
    • 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!
  • Schubert Calculus - S. L. Kleiman and Dan Laksov.
    • An introduction to Schubert calculus suitable for those of all ages. I am told the paper essentially only uses linear algebra!
  • Rational Isogenies of Prime Degree - Barry Mazur.
    • 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.
  • Esquisse d’une programme - Alexander Grothendieck.
    • 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.)
  • Géométrie algébraique et géométrie analytique - J.P. Serre.
    • 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.)
  • Limit linear series: Basic theory- David Eisenbud and Joe Harris.
    • 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.
  • Picard Groups of Moduli Problems - David Mumford.
    • This paper is essentially the origin of algebraic stacks.
  • The Structure of Algebraic Threefolds: An Introduction to Mori's Program - Janos Kollar
    • 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.
  • Cayley-Bacharach Formulas - Qingchun Ren, Jürgen Richter-Gebert, Bernd Sturmfels.
    • 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?.
  • On Varieties of Minimal Degree (A Centennial Approach) - David Eisenbud and Joe Harris.
    • 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.
  • The Gromov-Witten potential associated to a TCFT - Kevin J. Costello.
    • 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.)

Spring 2020

Date Speaker Title (click to see abstract)
January 29 Colin Crowley Lefschetz hyperplane section theorem via Morse theory
February 5 Asvin Gothandaraman An Introduction to Unirationality
February 12 Qiao He Title
February 19 Dima Arinkin Blowing down, blowing up: surface geometry
February 26 Connor Simpson Intro to toric varieties
March 4 Peter Title
March 11 Caitlyn Booms Title
March 25 Steven He Title
April 1 Vlad Sotirov Title
April 8 Maya Banks Title
April 15 Alex Mine Title
April 22 Ruofan Title
April 29 John Cobb Title

January 29

Colin Crowley
Title: Lefschetz hyperplane section theorem via Morse theory
Abstract: Morse theory allows you to learn about the topology of a manifold by studying the critical points of a nice function on the manifold. This perspective produces a nice proof of the theorem in the title, which concerns the homology of smooth projective varieties over C. I'll explain what the theorem says, say something about what Morse theory is and why it's related, and then finish with a neat example. I'm aiming to make this understandable to someone who's taken algebraic geometry 1 and topology 1.

February 5

Asvin Gothandaraman
Title: An introduction to unirationality
Abstract: I will introduce the notion of unirationality and show that cubic hypersurfaces are unirational (following Kollar). If time permits, I will also show that unirational varieties are simply connected.

February 12

Qiao He
Title:
Abstract:

February 19

Dima Arinkin
Title: Blowing down, blowing up: surface geometry
Abstract:A big question in algebraic geometry is how much one can change a variety without affecting it `generically'. More precisely, if two varieties are birational, how far can they be from being isomorphic?

The question is trivial for (smooth projective) curves: they are birational if and only if they are isomorphic. In higher dimension, the situation is much more interesting. The most fundamental operation are the `blowup', which is a kind of alteration of a variety within its birational isomorphism class, and its opposite, the blowdown.

In my talk, I will introduce blowups and discuss their properties. Then (time permitting) I would like to look deeper at the case of surfaces, where the combination of blowups and intersection theory provides a complete and beautiful picture. (If we do get to this point, I won't assume any knowledge of intersection theory: to an extent, this talk is my excuse to introduce it.)

February 26

Connor Simpson
Title: Intro to Toric Varieties
Abstract: A brief introduction to toric varieties: how to build them, formulas for computing topological data, toric blow-ups, and more.

March 4

Peter
Title:
Abstract:

March 11

Caitlyn Booms
Title:
Abstract:

March 25

Steven He
Title:
Abstract:

April 1

Vlad Sotirov
Title:
Abstract:

April 8

Maya Banks
Title:
Abstract:

April 15

Alex Mine
Title:
Abstract:

April 22

Ruofan
Title:
Abstract:

April 29

John Cobb
Title:
Abstract:


Organizers' Contact Info

Colin Crowley

David Wagner

Past Semesters

Fall 2019

Spring 2019

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015