https://www.math.wisc.edu/wiki/api.php?action=feedcontributions&user=Bboggess&feedformat=atomMath - User contributions [en]2019-06-25T18:13:16ZUser contributionsMediaWiki 1.28.3https://www.math.wisc.edu/wiki/index.php?title=NTSGrad_Spring_2019/Abstracts&diff=17355NTSGrad Spring 2019/Abstracts2019-04-21T16:44:50Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Spring 2019|here.]]<br />
<br />
== Jan 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Understanding the asymptotics of the mean square of the product of the Riemann zeta function with Dirichlet polynomials allows one to understand the distribution of values of L-functions. I will introduce the problem and describe several results from the paper of Bettin, Chandee and Radziwill who showed how to pass the so called <math>\theta=1/2</math> barrier for arbitrary Dirichlet polynomials. This will be a prep talk for Thursdays seminar.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representations of <math>GL_n(\mathbb{F}_q)</math> ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will discuss the irreducible representations of <math>GL_n(\mathbb{F}_q)</math>. In particular, I will discuss some ways in which we can understand the structure of representations of <math>GL_n(\mathbb{F}_q)</math> , such as parabolic inductions, Hopf algebra structure, and tensor ranks of representations. This is a preparatory talk for the upcoming talk on Thursday.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong Kim'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The integrality of the j-invariant on CM points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The j-function, a complex valued function whose inputs are elliptic curves over <math>\mathbb{C}</math>, classifies the isomorphism class of such elliptic curves. We show that, on elliptic curves with complex multiplication (CM), the j-function takes values which are algebraic integers.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 19 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''L-functions, Heegner Points and Euler Systems''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
This talk will be about the L-function of an elliptic curve. I will introduce the Gross-Zagier and the Waldspurger formulae, and try to explain why they are deep and useful for the study of L-functions of elliptic curves.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation stability and counting points on varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk I will describe the Church-Ellenberg-Farb philosophy of counting points on varieties over finite fields. I will talk about some connections between homological stability and asymptotics of point-counts. Time permitting, we will see how this fits into the framework of FI-modules.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''<math>p</math>-adic modular forms''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I will discuss Serre’s definition of <math>p</math>-adic modular forms. This is a preparatory talk for the Number Theory Seminar on Thursday.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The existence of infinitely many supersingular primes for every elliptic curve over <math>\mathbb{Q}</math>''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
For the GNTS on visitor's day, I want to present the work of Noam Elkies from his PhD thesis. I will try my best to make this talk completely self-contained, i.e. I will start with defining an elliptic curve and explain what supersingular means.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 2 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Weitong Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On <math>\ell</math>-torsion in class groups of number fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
According to Wei-Lun's request, I'll first introduce the big picture of the paper Nonvanishing of Hecke L-Functions and Bloch-Kato <math>p</math>-Selmer Groups, then focus on the quadratic case of the <math>\ell</math>-torsion in class groups.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 9 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sang Yup Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Ergodicity and Sarnak’s Conjecture on Randomness of the Mobius Function''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I’ll attempt to provide a number theorist’s explanation of flows and ergodicity, using one of our favorite spaces as an example. Then I’ll motivate the subject by presenting Sarnak’s conjecture on the randomness of the Mobius function and it’s corollaries.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Apr 16 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Niudun Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The march towards Malle's Conjecture''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In this talk, I will introduce Malle's conjecture and what is known about it. Then I will present an example using the most complicated group, <math>\mathbb{Z}/2\mathbb{Z}</math> to show how we count things in practice.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 23 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Asvin Gothandaraman'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Insufficiency of the Brauer Manin obstruction''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will sketch an example of Poonen showing that the Brauer-Manin obstruction is insufficient in general to detect the non existence of rational points.<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=NTSGrad_Spring_2019&diff=17354NTSGrad Spring 20192019-04-21T16:43:37Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B113 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | January 29<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Jan_29|Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 5<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/wisc.edu/spark483 Sun Woo Park]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_5| Representations of <math>GL_n(\mathbb{F}_q)</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 12<br />
| bgcolor="#F0B0B0" align="center" | Hyun Jong Kim<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_12| The integrality of the j-invariant on CM points]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 19<br />
| bgcolor="#F0B0B0" align="center" | Qiao He<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_19| L-functions, Heegner points and Euler systems]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 26<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_26| Representation stability and counting points on varieties]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | (Arizona Winter School)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_12| <math>p</math>-adic modular forms]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | (Spring Break)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_26| The existence of infinitely many supersingular primes for every elliptic curve over <math>\mathbb{Q}</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Weitong Wang<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_2| On <math>\ell</math>-torsion in class groups of number fields]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Sang Yup Han<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_9| Ergodicity and Sarnak’s Conjecture on Randomness of the Mobius Function]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 16<br />
| bgcolor="#F0B0B0" align="center" | Niudun Wang<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_16| The march towards Malle's conjecture]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_23|Insufficiency of the Brauer Manin obstruction]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Yu Fu<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| TBA<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=NTSGrad_Spring_2019/Abstracts&diff=17288NTSGrad Spring 2019/Abstracts2019-04-07T21:52:22Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Spring 2019|here.]]<br />
<br />
== Jan 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Understanding the asymptotics of the mean square of the product of the Riemann zeta function with Dirichlet polynomials allows one to understand the distribution of values of L-functions. I will introduce the problem and describe several results from the paper of Bettin, Chandee and Radziwill who showed how to pass the so called <math>\theta=1/2</math> barrier for arbitrary Dirichlet polynomials. This will be a prep talk for Thursdays seminar.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representations of <math>GL_n(\mathbb{F}_q)</math> ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will discuss the irreducible representations of <math>GL_n(\mathbb{F}_q)</math>. In particular, I will discuss some ways in which we can understand the structure of representations of <math>GL_n(\mathbb{F}_q)</math> , such as parabolic inductions, Hopf algebra structure, and tensor ranks of representations. This is a preparatory talk for the upcoming talk on Thursday.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong Kim'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The integrality of the j-invariant on CM points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The j-function, a complex valued function whose inputs are elliptic curves over <math>\mathbb{C}</math>, classifies the isomorphism class of such elliptic curves. We show that, on elliptic curves with complex multiplication (CM), the j-function takes values which are algebraic integers.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 19 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''L-functions, Heegner Points and Euler Systems''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
This talk will be about the L-function of an elliptic curve. I will introduce the Gross-Zagier and the Waldspurger formulae, and try to explain why they are deep and useful for the study of L-functions of elliptic curves.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation stability and counting points on varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk I will describe the Church-Ellenberg-Farb philosophy of counting points on varieties over finite fields. I will talk about some connections between homological stability and asymptotics of point-counts. Time permitting, we will see how this fits into the framework of FI-modules.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''<math>p</math>-adic modular forms''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I will discuss Serre’s definition of <math>p</math>-adic modular forms. This is a preparatory talk for the Number Theory Seminar on Thursday.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The existence of infinitely many supersingular primes for every elliptic curve over <math>\mathbb{Q}</math>''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
For the GNTS on visitor's day, I want to present the work of Noam Elkies from his PhD thesis. I will try my best to make this talk completely self-contained, i.e. I will start with defining an elliptic curve and explain what supersingular means.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 2 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Weitong Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''On <math>\ell</math>-torsion in class groups of number fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
According to Wei-Lun's request, I'll first introduce the big picture of the paper Nonvanishing of Hecke L-Functions and Bloch-Kato <math>p</math>-Selmer Groups, then focus on the quadratic case of the <math>\ell</math>-torsion in class groups.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Apr 9 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sang Yup Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Ergodicity and Sarnak’s Conjecture on Randomness of the Mobius Function''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I’ll attempt to provide a number theorist’s explanation of flows and ergodicity, using one of our favorite spaces as an example. Then I’ll motivate the subject by presenting Sarnak’s conjecture on the randomness of the Mobius function and it’s corollaries.<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=NTSGrad_Spring_2019&diff=17287NTSGrad Spring 20192019-04-07T21:51:10Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B113 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | January 29<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Jan_29|Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 5<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/wisc.edu/spark483 Sun Woo Park]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_5| Representations of <math>GL_n(\mathbb{F}_q)</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 12<br />
| bgcolor="#F0B0B0" align="center" | Hyun Jong Kim<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_12| The integrality of the j-invariant on CM points]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 19<br />
| bgcolor="#F0B0B0" align="center" | Qiao He<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_19| L-functions, Heegner points and Euler systems]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 26<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_26| Representation stability and counting points on varieties]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | (Arizona Winter School)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_12| <math>p</math>-adic modular forms]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | (Spring Break)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_26| The existence of infinitely many supersingular primes for every elliptic curve over <math>\mathbb{Q}</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Weitong Wang<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_2| On <math>\ell</math>-torsion in class groups of number fields]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Sang Yup Han<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Apr_9| Ergodicity and Sarnak’s Conjecture on Randomness of the Mobius Function]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 16<br />
| bgcolor="#F0B0B0" align="center" | Niudun Wang<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Yu Fu<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| TBA<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=NTSGrad_Spring_2019/Abstracts&diff=17209NTSGrad Spring 2019/Abstracts2019-03-25T00:28:05Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Spring 2019|here.]]<br />
<br />
== Jan 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Understanding the asymptotics of the mean square of the product of the Riemann zeta function with Dirichlet polynomials allows one to understand the distribution of values of L-functions. I will introduce the problem and describe several results from the paper of Bettin, Chandee and Radziwill who showed how to pass the so called <math>\theta=1/2</math> barrier for arbitrary Dirichlet polynomials. This will be a prep talk for Thursdays seminar.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representations of <math>GL_n(\mathbb{F}_q)</math> ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will discuss the irreducible representations of <math>GL_n(\mathbb{F}_q)</math>. In particular, I will discuss some ways in which we can understand the structure of representations of <math>GL_n(\mathbb{F}_q)</math> , such as parabolic inductions, Hopf algebra structure, and tensor ranks of representations. This is a preparatory talk for the upcoming talk on Thursday.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong Kim'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The integrality of the j-invariant on CM points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The j-function, a complex valued function whose inputs are elliptic curves over <math>\mathbb{C}</math>, classifies the isomorphism class of such elliptic curves. We show that, on elliptic curves with complex multiplication (CM), the j-function takes values which are algebraic integers.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 19 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''L-functions, Heegner Points and Euler Systems''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
This talk will be about the L-function of an elliptic curve. I will introduce the Gross-Zagier and the Waldspurger formulae, and try to explain why they are deep and useful for the study of L-functions of elliptic curves.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representation stability and counting points on varieties''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk I will describe the Church-Ellenberg-Farb philosophy of counting points on varieties over finite fields. I will talk about some connections between homological stability and asymptotics of point-counts. Time permitting, we will see how this fits into the framework of FI-modules.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''<math>p</math>-adic modular forms''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
In this talk, I will discuss Serre’s definition of <math>p</math>-adic modular forms. This is a preparatory talk for the Number Theory Seminar on Thursday.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Mar 26 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The existence of infinitely many supersingular primes for every elliptic curve over Q''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
<br />
For the GNTS on visitor's day, I want to present the work of Noam Elkies from his PhD theses. I will try my best to make this talk completely self-contained. I.e. I will start with defining an elliptic curve and explain what supersingular means.<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=NTSGrad_Spring_2019&diff=17208NTSGrad Spring 20192019-03-25T00:26:32Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B113 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | January 29<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Jan_29|Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 5<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/wisc.edu/spark483 Sun Woo Park]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_5| Representations of <math>GL_n(\mathbb{F}_q)</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 12<br />
| bgcolor="#F0B0B0" align="center" | Hyun Jong Kim<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_12| The integrality of the j-invariant on CM points]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 19<br />
| bgcolor="#F0B0B0" align="center" | Qiao He<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_19| L-functions, Heegner points and Euler systems]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 26<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/site/soumya3sankar/ Soumya Sankar]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_26| Representation stability and counting points on varieties]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | (Arizona Winter School)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_12| <math>p</math>-adic modular forms]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | (Spring Break)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Mar_26| The existence of infinitely many supersingular primes for every elliptic curve over Q]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | Weitong Wang<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | Sang Yup Han<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 16<br />
| bgcolor="#F0B0B0" align="center" | Niudun Wang<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | Yu Fu<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| TBA<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16995Graduate Algebraic Geometry Seminar2019-02-19T16:23:04Z<p>Bboggess: /* March 13 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying 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.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in 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!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* 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 2019 ==<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"| February 6<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 6| Heisenberg Groups and the Fourier Transform]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 13<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 13| DG potpourri]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 20<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 20| Completions of Noncatenary Local Domains and UFDs]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 27<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 27| Baker’s Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 6<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 6| Mason's Conjectures and Chow Rings of Matroids]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 13<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 13| Dial M_1,1 for moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 27<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 27| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 3<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 3| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 10<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 10| Kindergarten GAGA]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 17<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 17| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 24<br />
| bgcolor="#C6D46E"| Name<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 24| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 1<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 1| Orbifold Singular Cohomology]]<br />
|}<br />
</center><br />
<br />
== February 6 ==<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" | Title: Heisenberg Groups and the Fourier Transform<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{| style="color:black; 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" | Title: DG potpourri<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
[[File:Dg-meme.png]]<br />
|} <br />
</center><br />
<br />
== February 20 ==<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%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Completions of Noncatenary Local Domains and UFDs<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: We find necessary and sufficient conditions for a complete local ring to be the completion of a noncatenary local (Noetherian) domain, as well as necessary and sufficient conditions for it to be the completion of a noncatenary local (Noetherian) unique factorization domain. We use our first result to demonstrate a large class of quasi-excellent domains that are not excellent, as well as a large class of catenary domains that are not universally catenary. We use our second result to find a larger class of noncatenary local UFDs than was previously known, and we show that there is no bound on how noncatenary a UFD can be.<br />
|} <br />
</center><br />
<br />
== February 27 ==<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%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Baker's Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
|} <br />
</center><br />
<br />
== March 6 ==<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%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Mason's Conjectures and Chow Rings of Matroids<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
|} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{| style="color:black; 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" | Title: Dial M_1,1 for moduli<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: We will speculate wildly about what kind of object the moduli space of elliptic curves should be. I don't know what a stack is, and I promise not to try to define one.<br />
|} <br />
</center><br />
<br />
== March 27 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:<br />
|} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Name'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Orbifold Singular Cohomology<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
[https://www.math.wisc.edu/~moises/ Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16994Graduate Algebraic Geometry Seminar2019-02-19T16:21:08Z<p>Bboggess: /* Spring 2019 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying 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.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in 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!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* 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 2019 ==<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"| February 6<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 6| Heisenberg Groups and the Fourier Transform]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 13<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 13| DG potpourri]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 20<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 20| Completions of Noncatenary Local Domains and UFDs]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 27<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 27| Baker’s Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 6<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 6| Mason's Conjectures and Chow Rings of Matroids]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 13<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 13| Dial M_1,1 for moduli]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 27<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 27| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 3<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 3| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 10<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 10| Kindergarten GAGA]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 17<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 17| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 24<br />
| bgcolor="#C6D46E"| Name<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 24| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 1<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 1| Orbifold Singular Cohomology]]<br />
|}<br />
</center><br />
<br />
== February 6 ==<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" | Title: Heisenberg Groups and the Fourier Transform<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{| style="color:black; 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" | Title: DG potpourri<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
[[File:Dg-meme.png]]<br />
|} <br />
</center><br />
<br />
== February 20 ==<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%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Completions of Noncatenary Local Domains and UFDs<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: We find necessary and sufficient conditions for a complete local ring to be the completion of a noncatenary local (Noetherian) domain, as well as necessary and sufficient conditions for it to be the completion of a noncatenary local (Noetherian) unique factorization domain. We use our first result to demonstrate a large class of quasi-excellent domains that are not excellent, as well as a large class of catenary domains that are not universally catenary. We use our second result to find a larger class of noncatenary local UFDs than was previously known, and we show that there is no bound on how noncatenary a UFD can be.<br />
|} <br />
</center><br />
<br />
== February 27 ==<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%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Baker's Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
|} <br />
</center><br />
<br />
== March 6 ==<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%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Mason's Conjectures and Chow Rings of Matroids<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
|} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{| style="color:black; 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" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 27 ==<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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:<br />
|} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Name'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Orbifold Singular Cohomology<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
[https://www.math.wisc.edu/~moises/ Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16993Graduate Algebraic Geometry Seminar2019-02-19T16:20:54Z<p>Bboggess: /* Spring 2019 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:25pm<br />
<br />
'''Where:''' Van Vleck B317 (Spring 2019)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying 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.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:cbooms@wisc.edu Caitlyn] or [mailto:drwagner@math.wisc.edu David], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in 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!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* 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 2019 ==<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"| February 6<br />
| bgcolor="#C6D46E"| Vlad Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 6| Heisenberg Groups and the Fourier Transform]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 13<br />
| bgcolor="#C6D46E"| David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 13| DG potpourri]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 20<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 20| Completions of Noncatenary Local Domains and UFDs]]<br />
|-<br />
| bgcolor="#E0E0E0"| February 27<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#February 27| Baker’s Theorem]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 6<br />
| bgcolor="#C6D46E"| Connor Simpson<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 6| Mason's Conjectures and Chow Rings of Matroids]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 13<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 13| Dial M_1,1 for moduli.]]<br />
|-<br />
| bgcolor="#E0E0E0"| March 27<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#March 27| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 3<br />
| bgcolor="#C6D46E"| Colin Crowley<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 3| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 10<br />
| bgcolor="#C6D46E"| Alex Hof<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 10| Kindergarten GAGA]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 17<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 17| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| April 24<br />
| bgcolor="#C6D46E"| Name<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#April 24| Title]]<br />
|-<br />
| bgcolor="#E0E0E0"| May 1<br />
| bgcolor="#C6D46E"| Shengyuan Huang<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#May 1| Orbifold Singular Cohomology]]<br />
|}<br />
</center><br />
<br />
== February 6 ==<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" | Title: Heisenberg Groups and the Fourier Transform<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: I will discuss the relationship between Fourier transforms and the Heisenberg groups, with a view toward the discussion of line bundles on complex tori that appears in Polishchuk's book Abelian Varieties, Theta functions, and the Fourier transform.<br />
<br />
|} <br />
</center><br />
<br />
== February 13 ==<br />
<center><br />
{| style="color:black; 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" | Title: DG potpourri<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: I will explain how differential graded categories made their way into AG as a way to solve some of the inadequacies of the ordinary derived category. We will then give examples of the utility of DG techniques. <br />
[[File:Dg-meme.png]]<br />
|} <br />
</center><br />
<br />
== February 20 ==<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%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Completions of Noncatenary Local Domains and UFDs<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: We find necessary and sufficient conditions for a complete local ring to be the completion of a noncatenary local (Noetherian) domain, as well as necessary and sufficient conditions for it to be the completion of a noncatenary local (Noetherian) unique factorization domain. We use our first result to demonstrate a large class of quasi-excellent domains that are not excellent, as well as a large class of catenary domains that are not universally catenary. We use our second result to find a larger class of noncatenary local UFDs than was previously known, and we show that there is no bound on how noncatenary a UFD can be.<br />
|} <br />
</center><br />
<br />
== February 27 ==<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%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Baker's Theorem<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: As a follow up talk to last semester, I will state and prove Baker’s theorem, a classical theorem which uses Newton Polygons to count the genus of a given curve. I will also briefly sketch how one can use Newton polygons to understand resolution of singularities of a given curve over valuation rings.<br />
|} <br />
</center><br />
<br />
== March 6 ==<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%" | '''Connor Simpson'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Mason's Conjectures and Chow Rings of Matroids<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: A matroid is a combinatorial structure that abstracts many different notions of independence, including linear independence in a vector space. Mason's Conjectures are a series of three increasingly strong inequalities on certain numerical invariants of matroids, the weakest of which resisted proof for over 40 years until its resolution in 2015. However, in the years since, all of Mason's conjectures have become theorems!<br />
<br />
In this talk, we will introduce matroids and the Chow ring of a matroid, the amazing algebraic gadget used to prove Mason's first conjecture. Finally, outline the proof of Mason's second conjecture (work of our very own Botong Wang & coauthors).<br />
|} <br />
</center><br />
<br />
== March 13 ==<br />
<center><br />
{| style="color:black; 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" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== March 27 ==<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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract:<br />
|} <br />
</center><br />
<br />
== April 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Soumya Sankar'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== April 24 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Name'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: <br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== May 1 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Shengyuan Huang'''<br />
|-<br />
| bgcolor="#BCD2EE" | Title: Orbifold Singular Cohomology<br />
|-<br />
| bgcolor="#BCD2EE" | Abstract: <br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://sites.google.com/wisc.edu/cbooms/ Caitlyn Booms]<br />
<br />
[http://www.math.wisc.edu/~drwagner/ David Wagner]<br />
<br />
[https://www.math.wisc.edu/~moises/ Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2018 Fall 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=Reading_Seminar_2018-19&diff=16925Reading Seminar 2018-192019-02-14T17:52:28Z<p>Bboggess: /* Talk Schedule */</p>
<hr />
<div>==Overview==<br />
My (Daniel's) experience has been that reading seminars have diminishing returns: they run out of steam after about 8 lectures on a certain book, as everyone starts falling behind, etc. I was thinking aim broader (rather than deeper), covering 3 books, but with fewer lectures. My idea is to partly cover: Beauville's "Complex Algebraic Surfaces"; Atiyah's "K-theory" (1989 edition); and Harris and Morrison's "Moduli of Curves". We would do about 6-8 lectures on each. This allows us to reboot every two months, which I hope will be mentally refreshing and will allow people who have lost the thread of the book to rejoin. Anyways, it's an experiment!<br />
<br />
Some notes:<br />
<ul><br />
<li>Here is lecture notes from Ravi Vakil on Complex Algebraic Surfaces "http://math.stanford.edu/~vakil/02-245/index.html"<br />
<li> Each book will have a co-organizer: Wanlin Li for Beauville's book; Michael Brown for Atiyah's book; and Rachel Davis for Harris and Mumford's book. Thanks!</li><br />
<li>I left some "Makeup" dates in the schedule with the idea that we would most likely take a week off on those dates. But if we need to miss another date (because of a conflict with a special colloquium or some other event), then we can use those as makeup slots.</li><br />
</ul><br />
<br />
We are experimenting with lots of new formats in this year's seminar. If you aren't happy with how the reading seminar is going, please let one of the organizers (Daniel, Wanlin, Michael, or Rachel) know and we will do our best to get things back on a helpful track.<br />
<br />
==Time and Location==<br />
Talks will be on Fridays from 11:00-11:45 in B329. This semester, Daniel is planning to keep a VERY HARD watch on the clock.<br />
<br />
== Talk Schedule ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | sections<br />
<br />
|-<br />
|September 7<br />
|Wanlin Li<br />
|Beauville I<br />
|-<br />
|September 14<br />
|Rachel Davis<br />
|Beauville II<br />
|-<br />
|September 21<br />
|Brandon Boggess<br />
|Beauville II and III<br />
|-<br />
|September 28<br />
|Mao Li<br />
|Beauville III<br />
|-<br />
|October 5<br />
|Wendy Cheng<br />
|Beauville IV<br />
|-<br />
|October 12<br />
|Soumya Sankar<br />
|Beauville V<br />
|-<br />
|October 19<br />
|David Wagner<br />
|Beauville V and VI<br />
|-<br />
|October 26<br />
|Dan Corey<br />
|Beauville VII and VIII<br />
|-<br />
|November 2<br />
|No Meeting<br />
|Break<br />
|-<br />
|November 9<br />
|Michael Brown<br />
|Atiyah 1 (Overview of goals of the seminar, Section 2.1) <br />
|-<br />
|November 16<br />
|Asvin Gothandaraman<br />
|Atiyah 2 (Section 2.2)<br />
|-<br />
|November 23<br />
|NO MEETING<br />
|Thanksgiving<br />
|-<br />
|November 30<br />
|NO MEETING<br />
|<br />
|-<br />
|SEMESETER BREAK<br />
|No meetings<br />
|<br />
|-<br />
|January 25<br />
|Daniel Erman<br />
|Atiyah 3 (Section 2.5: Examples)<br />
|-<br />
|February 1<br />
|Rachel Davis<br />
|Atiyah 4 (Section 2.3: Bott periodicity)<br />
|-<br />
|February 8<br />
|Michael Brown<br />
|Atiyah 5 (Thom isomorphism)<br />
|-<br />
|February 15<br />
|Mao Li<br />
|Algebraic K theory, Localization theorem and flag variety.<br />
|-<br />
|February 22<br />
|No Meeting<br />
|<br />
|-<br />
|March 1<br />
| Juliette Bruce<br />
|Moduli 1<br />
|-<br />
|March 8<br />
|Niudun Wang<br />
|Moduli 2<br />
|-<br />
|March 15<br />
|Rachel Davis<br />
|Moduli 3<br />
|-<br />
|March 22<br />
|NO MEETING<br />
|Spring recess<br />
|-<br />
|March 29<br />
|Michael Brown<br />
|Moduli 4<br />
|-<br />
|April 5<br />
|Brandon Boggess<br />
|Moduli 5<br />
|-<br />
|April 12<br />
|??<br />
|Moduli 6<br />
|-<br />
|April 19<br />
|??<br />
|Moduli 7<br />
|}<br />
<br />
==How to plan your talk==<br />
One key to giving good talks in a reading seminar is to know how to refocus the material that you read. Instead of going through the chapter lemma by lemma, you should ask: What is the main idea in this section? It could be a theorem, a definition, or even an example. But after reading the section, decide what the most important idea is and be sure to highlight early on.<br />
<br />
You will probably need to skip the proofs--and even the statements--of many of the lemmas and other results in the chapter. This is a good thing! The reason someone attends a talk, as opposed to just reading the material on their own, is because they want to see the material from the perspective of someone who has thought it about carefully.<br />
<br />
Also, make sure to give clear examples.<br />
<br />
<br />
==Feedback on talks==<br />
One of the goals for this semester is to help the speakers learn to give better talks. Here is our plan:<br />
<br />
<li> Feedback session: This is like a streamlined version of what creative writing workshops do. Every week, we reserve 15 minutes (12:35-12:50) for the entire audience to critique that week’s speaker. Comments will be friendly and constructive. A key rule is that the speaker is not allowed to speak until the last 5 minutes.</li><br />
<br />
<li> Partner: We assign a “partner” each week (usually the previous week's speaker). The partner will meet for 20-30 minutes with the speaker in advance to:<br />
<ol> Discuss a plan for the talk. Here the speaker can outline what they see as the main ideas, and the partner can share any wisdom gleaned from their experience the previous week. </ol><br />
<ol> Ask the speaker if there are any particular things that the speaker would like feedback on (e.g. pacing, boardwork, clarity of voice, etc.). </ol><br />
The partner would also take notes during the feedback session, to give the speaker a record of the conversation.<br />
</li><br />
<br />
This is very much an experiment, and while it might be intimidating at first, I actually think it could really help everyone (the speakers and the audience members too).</div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=NTSGrad_Spring_2019&diff=16892NTSGrad Spring 20192019-02-10T22:03:00Z<p>Bboggess: /* Spring 2019 Semester: Schedule */</p>
<hr />
<div>= Graduate Student Number Theory / Representation Theory Seminar, University of Wisconsin – Madison =<br />
<br />
*'''When:''' Tuesdays, 2:30 PM – 3:30 PM<br />
*'''Where:''' B113 Van Vleck<br />
<br />
The purpose of this seminar is to have a talk on each Tuesday by a graduate student to<br />
help orient ourselves for the [[NTS_Spring_2019_Semester| Number Theory Seminar]] talk on the following Thursday.<br />
These talks are generally aimed at beginning graduate students, and try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2019 Semester: Schedule =<br />
<br />
<center><br />
<br />
{| style="color:black; font-size:120%" border="0" cellpadding="14" cellspacing="5"<br />
|-<br />
| bgcolor="#D0D0D0" width="300" align="center"|'''Date'''<br />
| bgcolor="#F0A0A0" width="300" align="center"|'''Speaker''' (click for homepage)<br />
| bgcolor="#BCD2EE" width="300" align="center"|'''Title''' (click for abstract)<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | January 29<br />
| bgcolor="#F0B0B0" align="center" | Ewan Dalby<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Jan_29|Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Feb 5<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/wisc.edu/spark483 Sun Woo Park]<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_5| Representations of <math>GL_n(\mathbb{F}_q)</math>]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 12<br />
| bgcolor="#F0B0B0" align="center" | Hyun Jong Kim<br />
| bgcolor="#BCE2FE"| [[NTSGrad_Spring_2019/Abstracts#Feb_5| The integrality of the j-invariant on CM points]]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 19<br />
| bgcolor="#F0B0B0" align="center" | Qiao He<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | February 26<br />
| bgcolor="#F0B0B0" align="center" | Soumya Sankar<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 5<br />
| bgcolor="#F0B0B0" align="center" | (Arizona Winter School)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 12<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 19<br />
| bgcolor="#F0B0B0" align="center" | (Spring Break)<br />
| bgcolor="#BCE2FE"| No Talk<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | March 26<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 2<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 9<br />
| bgcolor="#F0B0B0" align="center" | [https://sites.google.com/wisc.edu/spark483 Sun Woo Park]<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 16<br />
| bgcolor="#F0B0B0" align="center" | Niudun Wang<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 23<br />
| bgcolor="#F0B0B0" align="center" | Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | April 30<br />
| bgcolor="#F0B0B0" align="center" | TBA<br />
| bgcolor="#BCE2FE"| TBA<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | May 7<br />
| bgcolor="#F0B0B0" align="center" | [https://www.math.wisc.edu/~bboggess/ Brandon Boggess]<br />
| bgcolor="#BCE2FE"| TBA<br />
<br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
= Organizer(s) =<br />
<br />
Brandon Boggess (bboggess@math.wisc.edu)<br />
<br />
Soumya Sankar (ssankar3@wisc.edu)<br />
<br />
<br />
== Former Organizers ==<br />
<br />
Brandon Alberts <br />
<br />
Megan Maguire <br />
<br />
Ryan Julian<br />
<br />
= Other Graduate NTS Pages =<br />
<br />
The seminar webpage for Fall 2018 is [[NTSGrad_Fall_2018|here]].<br><br />
The seminar webpage for Spring 2018 is [[NTSGrad_Spring_2018|here]].<br><br />
The seminar webpage for Fall 2017 is [[NTSGrad|here]].<br><br />
The seminar webpage for Spring 2017 is [[NTSGrad_Spring_2017|here]].<br><br />
The seminar webpage for Fall 2016 is [[NTSGrad_Fall_2016|here]]<br><br />
The seminar webpage for Spring 2016 is [[NTSGrad_Spring_2016|here]]<br><br />
The seminar webpage for Fall 2015, is [[NTSGrad_Fall_2015|here]].<br><br />
<br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=NTSGrad_Spring_2019/Abstracts&diff=16891NTSGrad Spring 2019/Abstracts2019-02-10T22:01:44Z<p>Bboggess: </p>
<hr />
<div>This page contains the titles and abstracts for talks scheduled in the Spring 2019 semester. To go back to the main GNTS page, click [[NTSGrad_Spring 2019|here.]]<br />
<br />
== Jan 29 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Approximating the mean square of the product of the Riemann zeta function with Dirichlet polynomials ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Understanding the asymptotics of the mean square of the product of the Riemann zeta function with Dirichlet polynomials allows one to understand the distribution of values of L-functions. I will introduce the problem and describe several results from the paper of Bettin, Chandee and Radziwill who showed how to pass the so called <math>\theta=1/2</math> barrier for arbitrary Dirichlet polynomials. This will be a prep talk for Thursdays seminar.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 5 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Sun Woo Park'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Representations of <math>GL_n(\mathbb{F}_q)</math> ''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
I will discuss the irreducible representations of <math>GL_n(\mathbb{F}_q)</math>. In particular, I will discuss some ways in which we can understand the structure of representations of <math>GL_n(\mathbb{F}_q)</math> , such as parabolic inductions, Hopf algebra structure, and tensor ranks of representations. This is a preparatory talk for the upcoming talk on Thursday.<br />
<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Feb 12 ==<br />
<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Hyun Jong Kim'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The integrality of the j-invariant on CM points''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The j-function, a complex valued function whose inputs are elliptic curves over <math>\mathbb{C}</math>, classifies the isomorphism class of such elliptic curves. We show that, on elliptic curves with complex multiplication (CM), the j-function takes values which are algebraic integers.<br />
<br />
|} <br />
</center><br />
<br />
<br></div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16275Graduate Algebraic Geometry Seminar2018-10-25T14:24:23Z<p>Bboggess: /* October 31 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying 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.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in 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!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* 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"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov/David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner/Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| TBD]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 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.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<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: How to Parameterize Elliptic Curves and Influence People<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 7 ==<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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 14 ==<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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 21 ==<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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 7 ==<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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; 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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=Graduate_Algebraic_Geometry_Seminar&diff=16274Graduate Algebraic Geometry Seminar2018-10-25T14:23:35Z<p>Bboggess: /* Spring 2017 */</p>
<hr />
<div>'''<br />
'''When:''' Wednesdays 4:10pm<br />
<br />
'''Where:''' Van Vleck B215 (Fall 2018)<br />
[[Image:cat.jpg|thumb|220px| | Lizzie the OFFICIAL mascot of GAGS!!]]<br />
<br />
'''Who:''' All undergraduate and graduate students interested in algebraic geometry, commutative algebra, and related fields are welcome to attend.<br />
<br />
'''Why:''' The purpose of this seminar is to learn algebraic geometry and commutative algebra by giving and listening to talks in a informal setting. Talks are typically accessible to beginning graduate students and take many different forms. Sometimes people present an interesting paper they find. Other times people give a prep talk for the Friday Algebraic Geometry Seminar. Other times people give a series of talks on a topic they have been studying 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.<br />
<br />
'''How:''' If you want to get emails regarding time, place, and talk topics ('''which are often assigned quite last minute''') add yourself to the gags mailing list: gags@lists.wisc.edu. The list registration page is [https://admin.lists.wisc.edu/index.php?p=11&l=gags here].<br />
'''<br />
<br />
== Organize the seminar! ==<br />
<br />
'''This could be you writing this wiki page! Soon (Spring 2019) we will need volunteers to organize the seminar!! Why not start now?'''<br />
<br />
== Give a talk! ==<br />
We need volunteers to give talks this semester. If you're interested contact [mailto:moises@math.wisc.edu Moisés], or just add yourself to the list (though in that case we might move your talk later without your permission). Beginning graduate students are particularly encouraged to give a talk, since it's a great way to get your feet wet with the material.<br />
<br />
<br />
<br />
== Being an audience member ==<br />
The goal of GAGS is to create a safe and comfortable space inclusive of all who wish to expand their knowledge of algebraic geometry and commutative algebra. In order to promote such an environment in addition to the standard expectations of respect/kindness all participants are asked to following the following guidelines:<br />
* Do Not Speak For/Over the Speaker: <br />
* Ask Questions Appropriately: <br />
<br />
==The List of Topics that we Made February 2018==<br />
<br />
On February 21st of the Month of February of The 2018th Year of the Seventh Age of The Sun, the People Present at GAGS Compiled Ye Followinge Liste of Topics They Wished to Hear Aboute:<br />
<br />
Feel free to edit the list and/or add references to learn this stuff from. Since then, we've succeeded in talking about some of these, which doesn't mean there shouldn't be another talk. Ask around or look at old semester's websites.<br />
<br />
* Schubert Calculus, aka how many lines intersect four given lines in 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!<br />
<br />
* Kindergarten GAGA. GAGA stands for Algebraic Geometry - Analytic Geometry. Serre wrote a famous paper explaining how the two are related, and you could give an exposition suitable to kindergardeners.<br />
<br />
* Katz and Mazur explanation of what a modular form is. What is it?<br />
<br />
* Kindergarten moduli of curves.<br />
<br />
* What is a dualizing sheaf? What is a dualizing complex? What is Serre duality? What is local duality? Can local duality help us understand Serre duality?<br />
<br />
* Generalizations of Riemann - Roch. (Grothendieck - Riemann - Roch? Hirzebruch - Riemann - Roch?)<br />
<br />
* Hodge theory for babies<br />
<br />
* What is a Néron model?<br />
<br />
* What is a crystal? What does it have to do with D-modules? [http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Nov17-19(Crystals).pdf Here's an encouragingly short set of notes on it].<br />
<br />
* What and why is a dessin d'enfants?<br />
<br />
* DG Schemes.<br />
<br />
<br />
==Ed Dewey's Wish List Of Olde==<br />
<br />
Back in the day Ed and Nathan made this list of topics they wanted to hear. They all sound super duper cool, but it's also true that they had many years of AG behind their backs, so this list might not be very representative of what the GAGS audience wants to hear bout.<br />
<br />
Here are the topics we're '''DYING''' to learn about! Please consider looking into one of these topics and giving one or two GAGS talks.<br />
<br />
===Specifically Vague Topics===<br />
* 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"| September 12<br />
| bgcolor="#C6D46E"| Moisés Herradón Cueto<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Hodge Theory: One hour closer to understanding what it's about]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 19<br />
| bgcolor="#C6D46E"| Caitlyn Booms<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 12| Linear Resolutions of Edge Ideals]]<br />
|-<br />
| bgcolor="#E0E0E0"| September 26<br />
| bgcolor="#C6D46E"| Qiao He<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#September 26| An Elementary Introduction to Geometric Langlands]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 3<br />
| bgcolor="#C6D46E"| Wanlin Li<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 3| Gonality of Curves and More]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 10<br />
| bgcolor="#C6D46E"| Ewan Dalby<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 10| A Gentle introduction to Grothendieck's Galois theory]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 17<br />
| bgcolor="#C6D46E"| Johnnie Han<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 17| Schubert Calculus]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 24<br />
| bgcolor="#C6D46E"| Solly Parenti<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 24| Quadratic Polynomials]]<br />
|-<br />
| bgcolor="#E0E0E0"| October 31<br />
| bgcolor="#C6D46E"| Brandon Boggess<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#October 31| How to Parameterize Elliptic Curves and Influence People]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 7<br />
| bgcolor="#C6D46E"| Vladimir Sotirov/David Wagner<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 7| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 14<br />
| bgcolor="#C6D46E"| David Wagner/Vladimir Sotirov<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 14| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 21<br />
| bgcolor="#C6D46E"| A turkey/Smallpox<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 21| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| November 28<br />
| bgcolor="#C6D46E"| Asvin Gothandaraman<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#November 30| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 5<br />
| bgcolor="#C6D46E"| Soumya Sankar<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 5| TBD]]<br />
|-<br />
| bgcolor="#E0E0E0"| December 12<br />
| bgcolor="#C6D46E"| Sun Woo Park<br />
| bgcolor="#BCE2FE"|[[Graduate Algebraic Geometry Seminar#December 12| TBD]]<br />
|}<br />
</center><br />
<br />
== September 12 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Moisés Herradón Cueto'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Hodge Theory: One hour closer to understanding what it's about<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Following the request for baby Hodge theory from our meeting last semester, I will speak for one hour about Hodge theory, starting from the beginning of times, as they say. There will be d's, dbar's, Kählers and Hodge structures, but that's the extent of my promises. It will be a joyful time!<br />
|} <br />
</center><br />
<br />
== September 19 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Linear Resolutions of Edge Ideals<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We will briefly discuss monomial ideals in the multivariate polynomial ring over an algebraically closed field and some of their properties, including what it means for an ideal to have a linear resolution. Then we will talk about graphs on n vertices and their corresponding edge ideals, which are a particular kind of monomial ideal. Together, these will help us understand Froberg's Theorem, which says exactly when an edge ideal has a linear resolution. This talk will focus on a few computational examples and will end with some open questions and conjectures related to the presented material.<br />
|} <br />
</center><br />
<br />
== September 26 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: An Elementary Introduction to Geometric Langlands<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will start with the a rough statement of global langlands correspondence which suggest some correspondence between Galois representation and automorphic representation. Given this motivation, I will try to explain how can we replace both Galois side and Automorphic side with algebraic geometry objects. After that I will sketch what the geometric Langlands should be in this context.<br />
|} <br />
</center><br />
<br />
== October 3 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Wanlin Li'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Gonality of Curves and More<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
I will introduce an invariant, gonality of curves, from the definition, properties to its applications on modular curves. <br />
|} <br />
</center><br />
<br />
== October 10 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ewan Dalby'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: A Gentle introduction to Grothendiecks Galois theory<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
We all know and love Galois theory as it applies to fields and their extensions. Grothendieck, as always, showed how to lever the same ideas much more generally in algebraic geometry. I will try to explain how things work for the case of commutative rings in an "elementary" fashion.<br />
|} <br />
</center><br />
<br />
== October 17 ==<br />
<center><br />
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"<br />
|-<br />
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Johnnie Han'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Schubert Calculus<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
In this talk, we’ll go back to 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.<br />
<br />
|} <br />
</center><br />
<br />
== October 24 ==<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%" | '''Solly Parenti'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: Quadratic Polynomials<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
Quadratic polynomials have been studied forever. You can't just like play around with them and expect cool exciting math things like modular forms or special values of L-functions to show up, that would be ridiculous.<br />
|} <br />
</center><br />
<br />
== October 31 ==<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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 7 ==<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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 14 ==<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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 21 ==<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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 28 ==<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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== November 7 ==<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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 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%" | '''TBD'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Title: TBD<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Abstract: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== December 12 ==<br />
<center><br />
{| style="color:black; 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: <br />
<br />
TBD<br />
|} <br />
</center><br />
<br />
== Organizers' Contact Info ==<br />
<br />
[https://www.math.wisc.edu/~moises Moisés Herradón Cueto]<br />
<br />
== Past Semesters ==<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2018 Spring 2018]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2017 Fall 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2017 Spring 2017]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Fall_2016 Fall 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_Spring_2016 Spring 2016]<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Graduate_Algebraic_Geometry_Seminar_(Fall_2015) Fall 2015]</div>Bboggesshttps://www.math.wisc.edu/wiki/index.php?title=Abelian_Varieties_2018&diff=15151Abelian Varieties 20182018-02-19T15:11:26Z<p>Bboggess: /* Talk Schedule */</p>
<hr />
<div>== Overview ==<br />
This reading seminar will cover Kempf's "Complex Abelian Varieties and Theta Functions" book. Talks will be Mondays, 4:00-4:50 in Room B139.<br />
<br />
We can try to cover Chapters 1-7 and Chapter 11 and maybe some topics from the other chapters of Birkenhake and Lange's "Complex Abelian Varieties" as time permits.<br />
<br />
== Talk Schedule ==<br />
The following schedule might be adjusted as we go, depending on whether it seems too fast or not.<br />
<br />
Here is the [[https://www.math.wisc.edu/wiki/images/TOC.pdf Table of Contents]] of Kempf's book.<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | sections<br />
<br />
|-<br />
|February 7<br />
|Rachel Davis<br />
|1.1-1.3<br />
|-<br />
|February 12<br />
|Soumya Sankar<br />
|1.4-1.5<br />
|-<br />
|February 19<br />
|Michael Brown<br />
|2.1-2.2<br />
|-<br />
|February 26<br />
|Solly Parenti<br />
|2.3-2.4<br />
|-<br />
|March 5<br />
|TBD<br />
|3.1-3.3<br />
|-<br />
|March 12<br />
|Moisés Herradón Cueto<br />
|3.4-3.6<br />
|-<br />
|March 19<br />
|Brandon Boggess<br />
|4<br />
|-<br />
|March 26<br />
|No meeting<br />
|Spring Break<br />
|-<br />
|April 2<br />
|Mao Li<br />
|5.1-5.3<br />
|-<br />
|April 9<br />
|TBD<br />
|5.3-5.5<br />
|-<br />
|April 16<br />
|TBD<br />
|6<br />
|-<br />
|April 23<br />
|TBD<br />
|7<br />
|-<br />
|April 30<br />
|TBD<br />
|11<br />
|-<br />
|May 7<br />
|TBD<br />
|???<br />
|-<br />
|}</div>Bboggess