https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Mmaguire2&feedformat=atomUW-Math Wiki - User contributions [en]2024-03-19T14:03:54ZUser contributionsMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php?title=AMS_Student_Chapter_Seminar&diff=13440AMS Student Chapter Seminar2017-03-01T15:41:49Z<p>Mmaguire2: /* March 1, Megan Maguire */</p>
<hr />
<div>The AMS Student Chapter Seminar is an informal, graduate student-run seminar on a wide range of mathematical topics. Pastries (usually donuts) will be provided.<br />
<br />
* '''When:''' Wednesdays, 3:30 PM – 4:00 PM<br />
* '''Where:''' Van Vleck, 9th floor lounge (unless otherwise announced)<br />
* '''Organizers:''' [https://www.math.wisc.edu/~hast/ Daniel Hast], [https://www.math.wisc.edu/~mrjulian/ Ryan Julian], Cullen McDonald, [https://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
<br />
Everyone is welcome to give a talk. To sign up, please contact one of the organizers with a title and abstract. Talks are 30 minutes long and should avoid assuming significant mathematical background beyond first-year graduate courses.<br />
<br />
The schedule of talks from past semesters can be found [[AMS Student Chapter Seminar, previous semesters|here]].<br />
<br />
== Spring 2017 ==<br />
<br />
=== January 25, Brandon Alberts ===<br />
<br />
Title: Ultraproducts - they aren't just for logicians<br />
<br />
Abstract: If any of you have attended a logic talk (or one of Ivan's donut seminar talks) you may have learned about ultraproducts as a weird way to mash sets together to get bigger sets in a nice way. Something particularly useful to set theorists, but maybe not so obviously useful to the rest of us. I will give an accessible introduction to ultraproducts and motivate their use in other areas of mathematics.<br />
<br />
=== February 1, Megan Maguire ===<br />
<br />
Title: Hyperbolic crochet workshop<br />
<br />
Abstract: TBA<br />
<br />
=== February 8, Cullen McDonald ===<br />
<br />
=== February 15, Paul Tveite ===<br />
<br />
Title: Fun with Hamel Bases!<br />
<br />
Abstract: If we view the real numbers as a vector field over the rationals, then of course they have a basis (assuming the AOC). This is called a Hamel basis and allows us to do some cool things. Among other things, we will define two periodic functions that sum to the identity function.<br />
<br />
=== February 22, Wil Cocke ===<br />
<br />
Title: Practical Graph Isomorphism<br />
<br />
Abstract: Some graphs are different and some graphs are the same. Sometimes graphs differ only in name. When you give me a graph, you've picked an order. But, is it the same graph across every border?<br />
<br />
=== March 1, Megan Maguire ===<br />
<br />
Title: I stole this talk from Jordan.<br />
<br />
Abstract: Stability is cool! And sometimes things we think don't have stability secretly do. This is an abridged version of a very cool talk I've seen Jordan give a couple times. All credit goes to him. Man, I should have stolen his abstract too.<br />
<br />
=== March 7, Liban Mohamed ===<br />
<br />
Title: Strichartz Estimates from Qualitative to Quantitative<br />
<br />
Abstract: Strichartz estimates are inequalities that give one way understand the decay of solutions to dispersive PDEs. This talk is an attempt to reconcile the formal statements with physical intuition.<br />
<br />
=== March 15, Zachary Charles ===<br />
<br />
Title: Netflix Problem and Chill<br />
<br />
Abstract: How are machine learning, matrix analysis, and Napoleon Dynamite related? Come find out!<br />
<br />
=== March 29, TBA ===<br />
<br />
=== April 5, TBA ===<br />
<br />
=== April 12, TBA ===<br />
<br />
=== April 19, TBA ===<br />
<br />
=== April 26, TBA ===<br />
<br />
=== May 3, TBA ===</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10838NTSGrad Fall 2015/Abstracts2015-12-07T06:17:18Z<p>Mmaguire2: /* Dec 08 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''How I accidentally became a topologist: a cautionary tale''<br />
|-<br />
| bgcolor="#BCD2EE" | The Grothendieck Ring of Varieties is super cool (that's a technical term) and can be used to predict things about the complex topology of complex varieties (like what their Betti numbers should be). However, you can't prove these topological things just using the Grothendieck ring. You have to get down and dirty with topology. It's still pretty cool.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | Start with a number field K. Let K_1 be the Hilbert class field of K. Let K_2 be the Hilbert class field of K_1. If we keep defining K_n<br />
like this, does it eventually stabilize? In 1964, Golod and<br />
Shafarevich proved that this tower of fields can be infinite. The<br />
proof of this fact comes down to some facts about group theory and<br />
more specifically group cohomology. This talk will be an introduction<br />
to group cohomology and we'll even try to prove Golod and<br />
Shafarevich's result if we have time.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 24 ==<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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to Singular Moduli''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The values of j-function at imaginary quadratic argument are called singular moduli as they correspond to the j-invariants of singular elliptic curves. These singular moduli turn out to be highly divisible as predicted by a remarkable theorem of Gross and Zagier. I will give a brief introduction of singular moduli and some interesting results about them.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 08 ==<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%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generating random factored numbers and ideals, easily''<br />
|-<br />
| bgcolor="#BCD2EE" | Say we want to generate a number, up to some bound N, uniformly at random, but we also want to know its factorization. We could generate a number and then factor it, but factoring isn't known to be polynomial time. In his dissertation, Eric Bach gave a polynomial time way to do this. We will present an alternative polynomial time algorithm for generating a number and its factorization uniformly at random. We will then extend this to the problem of generating ideals in number fields and their factorization uniformly at random, in polynomial time. If time permits, we will discuss how to extend this to arbitrary number fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 15 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=10837NTSGrad2015-12-07T06:16:42Z<p>Mmaguire2: /* Fall 2015 Semester */</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:''' Van Vleck B119<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_08 ''Chevallay Groups'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_15 ''The Important Questions'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 29 <br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~eramos/ Eric Ramos]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_29 ''Generalized Representation Stability and FI_d-modules'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 20<br />
| bgcolor="#F0B0B0" align="center" |[http://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_20 ''Untitled'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mmaguire2/ Megan Maguire] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_27 ''How I accidentally became a topologist: a cautionary tale'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_3 ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~yu/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_24 ''Introduction to Singular Moduli'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_01 ''Number theory and modern cryptography'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 8<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_08 ''Generating random factored numbers and ideals, easily'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 15<br />
| bgcolor="#F0B0B0" align="center" | Jiuya Wang<br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=10836NTSGrad2015-12-07T06:16:04Z<p>Mmaguire2: /* Fall 2015 Semester */</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:''' Van Vleck B119<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_08 ''Chevallay Groups'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_15 ''The Important Questions'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 29 <br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~eramos/ Eric Ramos]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_29 ''Generalized Representation Stability and FI_d-modules'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 20<br />
| bgcolor="#F0B0B0" align="center" |[http://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_20 ''Untitled'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mmaguire2/ Megan Maguire] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_27 ''How I accidentally became a topologist: a cautionary tale<br />
'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_3 ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~yu/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_24 ''Introduction to Singular Moduli'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_01 ''Number theory and modern cryptography'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 8<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_08 ''Generating random factored numbers and ideals, easily'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 15<br />
| bgcolor="#F0B0B0" align="center" | Jiuya Wang<br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=10812NTSGrad2015-12-01T18:11:43Z<p>Mmaguire2: /* Fall 2015 Semester */</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:''' Van Vleck B119<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_08 ''Chevallay Groups'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_15 ''The Important Questions'']<br />
<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 29 <br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~eramos/ Eric Ramos]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_29 ''Generalized Representation Stability and FI_d-modules'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 20<br />
| bgcolor="#F0B0B0" align="center" |[http://www.math.wisc.edu/~wanlin/ Wanlin Li]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_20 ''Untitled'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mmaguire2/ Megan Maguire] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_27 ''How I accidentally became a topologist: a cautionary tale<br />
'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_3 ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~yu/ Peng Yu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_24 ''Introduction to Singular Moduli'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Dec_01 ''Number theory and modern cryptography'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 8<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 15<br />
| bgcolor="#F0B0B0" align="center" | Jiuya Wang<br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10811NTSGrad Fall 2015/Abstracts2015-12-01T18:11:26Z<p>Mmaguire2: /* Dec 08 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''How I accidentally became a topologist: a cautionary tale''<br />
|-<br />
| bgcolor="#BCD2EE" | The Grothendieck Ring of Varieties is super cool (that's a technical term) and can be used to predict things about the complex topology of complex varieties (like what their Betti numbers should be). However, you can't prove these topological things just using the Grothendieck ring. You have to get down and dirty with topology. It's still pretty cool.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | Start with a number field K. Let K_1 be the Hilbert class field of K. Let K_2 be the Hilbert class field of K_1. If we keep defining K_n<br />
like this, does it eventually stabilize? In 1964, Golod and<br />
Shafarevich proved that this tower of fields can be infinite. The<br />
proof of this fact comes down to some facts about group theory and<br />
more specifically group cohomology. This talk will be an introduction<br />
to group cohomology and we'll even try to prove Golod and<br />
Shafarevich's result if we have time.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 24 ==<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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to Singular Moduli''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The values of j-function at imaginary quadratic argument are called singular moduli as they correspond to the j-invariants of singular elliptic curves. These singular moduli turn out to be highly divisible as predicted by a remarkable theorem of Gross and Zagier. I will give a brief introduction of singular moduli and some interesting results about them.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 08 ==<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%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
== Dec 15 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10810NTSGrad Fall 2015/Abstracts2015-12-01T18:02:05Z<p>Mmaguire2: /* Dec 09 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''How I accidentally became a topologist: a cautionary tale''<br />
|-<br />
| bgcolor="#BCD2EE" | The Grothendieck Ring of Varieties is super cool (that's a technical term) and can be used to predict things about the complex topology of complex varieties (like what their Betti numbers should be). However, you can't prove these topological things just using the Grothendieck ring. You have to get down and dirty with topology. It's still pretty cool.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | Start with a number field K. Let K_1 be the Hilbert class field of K. Let K_2 be the Hilbert class field of K_1. If we keep defining K_n<br />
like this, does it eventually stabilize? In 1964, Golod and<br />
Shafarevich proved that this tower of fields can be infinite. The<br />
proof of this fact comes down to some facts about group theory and<br />
more specifically group cohomology. This talk will be an introduction<br />
to group cohomology and we'll even try to prove Golod and<br />
Shafarevich's result if we have time.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 24 ==<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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to Singular Moduli''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The values of j-function at imaginary quadratic argument are called singular moduli as they correspond to the j-invariants of singular elliptic curves. These singular moduli turn out to be highly divisible as predicted by a remarkable theorem of Gross and Zagier. I will give a brief introduction of singular moduli and some interesting results about them.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 08 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10809NTSGrad Fall 2015/Abstracts2015-12-01T18:01:36Z<p>Mmaguire2: /* Nov 25 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''How I accidentally became a topologist: a cautionary tale''<br />
|-<br />
| bgcolor="#BCD2EE" | The Grothendieck Ring of Varieties is super cool (that's a technical term) and can be used to predict things about the complex topology of complex varieties (like what their Betti numbers should be). However, you can't prove these topological things just using the Grothendieck ring. You have to get down and dirty with topology. It's still pretty cool.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | Start with a number field K. Let K_1 be the Hilbert class field of K. Let K_2 be the Hilbert class field of K_1. If we keep defining K_n<br />
like this, does it eventually stabilize? In 1964, Golod and<br />
Shafarevich proved that this tower of fields can be infinite. The<br />
proof of this fact comes down to some facts about group theory and<br />
more specifically group cohomology. This talk will be an introduction<br />
to group cohomology and we'll even try to prove Golod and<br />
Shafarevich's result if we have time.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 24 ==<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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to Singular Moduli''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The values of j-function at imaginary quadratic argument are called singular moduli as they correspond to the j-invariants of singular elliptic curves. These singular moduli turn out to be highly divisible as predicted by a remarkable theorem of Gross and Zagier. I will give a brief introduction of singular moduli and some interesting results about them.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10808NTSGrad Fall 2015/Abstracts2015-12-01T18:01:22Z<p>Mmaguire2: /* Nov 18 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''How I accidentally became a topologist: a cautionary tale''<br />
|-<br />
| bgcolor="#BCD2EE" | The Grothendieck Ring of Varieties is super cool (that's a technical term) and can be used to predict things about the complex topology of complex varieties (like what their Betti numbers should be). However, you can't prove these topological things just using the Grothendieck ring. You have to get down and dirty with topology. It's still pretty cool.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | Start with a number field K. Let K_1 be the Hilbert class field of K. Let K_2 be the Hilbert class field of K_1. If we keep defining K_n<br />
like this, does it eventually stabilize? In 1964, Golod and<br />
Shafarevich proved that this tower of fields can be infinite. The<br />
proof of this fact comes down to some facts about group theory and<br />
more specifically group cohomology. This talk will be an introduction<br />
to group cohomology and we'll even try to prove Golod and<br />
Shafarevich's result if we have time.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 24 ==<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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to Singular Moduli''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The values of j-function at imaginary quadratic argument are called singular moduli as they correspond to the j-invariants of singular elliptic curves. These singular moduli turn out to be highly divisible as predicted by a remarkable theorem of Gross and Zagier. I will give a brief introduction of singular moduli and some interesting results about them.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10807NTSGrad Fall 2015/Abstracts2015-12-01T18:01:09Z<p>Mmaguire2: /* Nov 11 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''How I accidentally became a topologist: a cautionary tale''<br />
|-<br />
| bgcolor="#BCD2EE" | The Grothendieck Ring of Varieties is super cool (that's a technical term) and can be used to predict things about the complex topology of complex varieties (like what their Betti numbers should be). However, you can't prove these topological things just using the Grothendieck ring. You have to get down and dirty with topology. It's still pretty cool.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | Start with a number field K. Let K_1 be the Hilbert class field of K. Let K_2 be the Hilbert class field of K_1. If we keep defining K_n<br />
like this, does it eventually stabilize? In 1964, Golod and<br />
Shafarevich proved that this tower of fields can be infinite. The<br />
proof of this fact comes down to some facts about group theory and<br />
more specifically group cohomology. This talk will be an introduction<br />
to group cohomology and we'll even try to prove Golod and<br />
Shafarevich's result if we have time.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 24 ==<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%" | '''Peng Yu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Introduction to Singular Moduli''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The values of j-function at imaginary quadratic argument are called singular moduli as they correspond to the j-invariants of singular elliptic curves. These singular moduli turn out to be highly divisible as predicted by a remarkable theorem of Gross and Zagier. I will give a brief introduction of singular moduli and some interesting results about them.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10806NTSGrad Fall 2015/Abstracts2015-12-01T17:59:17Z<p>Mmaguire2: /* Nov 04 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''How I accidentally became a topologist: a cautionary tale''<br />
|-<br />
| bgcolor="#BCD2EE" | The Grothendieck Ring of Varieties is super cool (that's a technical term) and can be used to predict things about the complex topology of complex varieties (like what their Betti numbers should be). However, you can't prove these topological things just using the Grothendieck ring. You have to get down and dirty with topology. It's still pretty cool.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | Start with a number field K. Let K_1 be the Hilbert class field of K. Let K_2 be the Hilbert class field of K_1. If we keep defining K_n<br />
like this, does it eventually stabilize? In 1964, Golod and<br />
Shafarevich proved that this tower of fields can be infinite. The<br />
proof of this fact comes down to some facts about group theory and<br />
more specifically group cohomology. This talk will be an introduction<br />
to group cohomology and we'll even try to prove Golod and<br />
Shafarevich's result if we have time.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10805NTSGrad Fall 2015/Abstracts2015-12-01T17:58:41Z<p>Mmaguire2: /* Nov 3 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''How I accidentally became a topologist: a cautionary tale''<br />
|-<br />
| bgcolor="#BCD2EE" | The Grothendieck Ring of Varieties is super cool (that's a technical term) and can be used to predict things about the complex topology of complex varieties (like what their Betti numbers should be). However, you can't prove these topological things just using the Grothendieck ring. You have to get down and dirty with topology. It's still pretty cool.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | ''Golod-Shafarevich or: How I learned to Stop Worrying and Love Cohomology''<br />
|-<br />
| bgcolor="#BCD2EE" | Start with a number field K. Let K_1 be the Hilbert class field of K. Let K_2 be the Hilbert class field of K_1. If we keep defining K_n<br />
like this, does it eventually stabilize? In 1964, Golod and<br />
Shafarevich proved that this tower of fields can be infinite. The<br />
proof of this fact comes down to some facts about group theory and<br />
more specifically group cohomology. This talk will be an introduction<br />
to group cohomology and we'll even try to prove Golod and<br />
Shafarevich's result if we have time.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10804NTSGrad Fall 2015/Abstracts2015-12-01T17:57:39Z<p>Mmaguire2: /* Oct 27 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''How I accidentally became a topologist: a cautionary tale''<br />
|-<br />
| bgcolor="#BCD2EE" | The Grothendieck Ring of Varieties is super cool (that's a technical term) and can be used to predict things about the complex topology of complex varieties (like what their Betti numbers should be). However, you can't prove these topological things just using the Grothendieck ring. You have to get down and dirty with topology. It's still pretty cool.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10803NTSGrad Fall 2015/Abstracts2015-12-01T17:56:33Z<p>Mmaguire2: /* Oct 20 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10802NTSGrad Fall 2015/Abstracts2015-12-01T17:55:42Z<p>Mmaguire2: /* Oct 13 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10801NTSGrad Fall 2015/Abstracts2015-12-01T17:54:57Z<p>Mmaguire2: /* Sep 22 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 13 ==<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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10800NTSGrad Fall 2015/Abstracts2015-12-01T17:54:45Z<p>Mmaguire2: /* Oct 06 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 22 ==<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%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 13 ==<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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10799NTSGrad Fall 2015/Abstracts2015-12-01T17:53:49Z<p>Mmaguire2: /* Sep 29 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 22 ==<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%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Generalized Representation Stability and FI_d-modules.''<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 06 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 13 ==<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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10798NTSGrad Fall 2015/Abstracts2015-12-01T17:53:18Z<p>Mmaguire2: /* Sep 29 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 22 ==<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%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Generalized Representation Stability and FI_d-modules.<br />
|-<br />
| bgcolor="#BCD2EE" | Let FI denote the category of finite sets and injections.<br />
Representations of this category, known as FI-modules, have been shown<br />
to have incredible applications to topology and arithmetic statistics.<br />
More recently, Sam and Snowden have begun looking at a more general<br />
category, FI_d, whose objects are finite sets, and whose morphisms are<br />
pairs (f,g) of an injection f with a d-coloring of the compliment of<br />
the image of f. These authors discovered that while this category is<br />
very nearly FI, its representations are considerably more complicated.<br />
One way to simplify the theory is to use the combinatorics of FI_d and<br />
the symmetric groups to our advantage.<br />
<br />
In this talk we will approach the representation theory of FI_d using<br />
mostly combinatorial methods. As a result, we will be about to prove<br />
theorems which restrict the growth of these representations in terms<br />
of certain combinatorial criterion. The talk will be as self contained<br />
as possible. It should be of interest to anyone studying<br />
representation theory or algebraic combinatorics.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 06 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 13 ==<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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 01 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Number theory and modern cryptography<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This will be a survey-level talk. We'll start with the state of practical RSA and then discuss some cryptosystems that address security-related questions for which there isn't a known answer in the case of RSA. Time permitting, we'll also discuss applications of class field theory to one promising class of such systems. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=10767NTSGrad2015-11-20T02:22:51Z<p>Mmaguire2: /* Fall 2015 Semester */</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:''' Van Vleck B119<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_08 ''Chevallay Groups'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_15 ''The Important Questions'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 29 <br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 06<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~eramos/ Eric Ramos]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 20<br />
| bgcolor="#F0B0B0" align="center" |<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 27<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles] <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 10<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 17<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~yu/ Peng Yu]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 1<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 8<br />
| bgcolor="#F0B0B0" align="center" | Zachary Charles<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 15<br />
| bgcolor="#F0B0B0" align="center" | Jiuya Wang<br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10193NTSGrad Fall 2015/Abstracts2015-09-11T20:56:17Z<p>Mmaguire2: </p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 22 ==<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%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 06 ==<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%" | '''Daniel Ross'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" |<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 13 ==<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%" | '''Eric Ramos'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 20 ==<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%" | '''Zachary Charles'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 27 ==<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%" | <br />
|-<br />
| bgcolor="#BCD2EE" align="center" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 3 ==<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" | <br />
|-<br />
| bgcolor="#BCD2EE" | <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=10192NTSGrad2015-09-11T20:50:59Z<p>Mmaguire2: /* Fall 2015 Semester */</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:''' Van Vleck B119<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_08 ''Chevallay Groups'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_15 ''The Important Questions'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 29 <br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 06<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 13<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~eramos/ Eric Ramos]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 27<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 10<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 17<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~yu/ Peng Yu]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10188NTSGrad Fall 2015/Abstracts2015-09-11T20:42:20Z<p>Mmaguire2: /* Sep 09 */</p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 15 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Important Questions''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Did the Universe come from nothing? Why are we moral? Where did we come from? According to some signs on Bascom Hill these are the important questions in life. Sadly the poor person who made these signs does not know what the really important questions are: What is David Zureick-Brown going to saying in his NTS talk? How many rational points are on the projective curve given (in affine coordinates) by:<br />
$$y^2 = x^6 + 8x^5 + 22x^4 + 22x^3 + 5x^2 + 6x + 1?$$<br />
If you would like to be enlightened by the answers to these truly important questions come to my talk where everything will be illuminated… Or at least some of the background for Coleman and Chabauty’s method for finding rational points on curves will be discussed<br />
<br />
PS: The number of references to Elijah Wood will be bounded — just like the number of rational points on our curves.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Alternate Discriminants and Mass Formulas for Number Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Moments of prime polynomials in short intervals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Trouble with Sharblies''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Brandon Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''Yueke Hu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Mass equidistribution on modular curve of level N''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It was shown in previous works that the measure associated to holomorphic newforms of weight k and level q will tend weakly to the Haar measure on modular curve of level 1, as qk goes to infinity. In this talk I will show that this phenomenon is also true on modular curves of general level N.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Intro to Complex Dynamics''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Given a polynomial f(z) with complex coefficients, we can ask for which complex numbers p is the set {f(p), f(f(p)), f(f(f(p))),...} bounded, that is to ask which complex numbers have bounded forward orbit under f(z)? Alternatively we can turn the question around and ask for a fixed complex number p, for which (complex) polynomials is the forward orbit of p bounded? Finite? Periodic? These questions give the interesting fractal pictures many of you have probably seen. Amazingly many of the tools needed to approach these questions, arose well before computers allowed us to generate images like the one above. In this talk we will explore some of the basic tools and results of complex dynamics paying particular attention relations to number theory. The goal being to present some of the background material need for Laura DeMarco’s talk later in the week. (Also getting to see a really cool area of mathematics!)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=10187NTSGrad2015-09-11T20:38:53Z<p>Mmaguire2: /* Fall 2015 Semester */</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:''' Van Vleck B119<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_08 ''Chevallay Groups'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_15 ''The Important Questions'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 29 <br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 06<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 27<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 10<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 17<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~yu/ Peng Yu]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=10186NTSGrad2015-09-11T20:38:05Z<p>Mmaguire2: /* Fall 2015 Semester */</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:''' Van Vleck B119<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_08 ''Chevallay Groups'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_15 ''The Important Questions'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 29 <br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 06<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 27<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 10<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 17<br />
| bgcolor="#F0B0B0" align="center" | Daniel Hast<br />
| bgcolor="#BCE2FE"| [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~yu/ Peng Yu]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=10185NTSGrad2015-09-11T20:31:04Z<p>Mmaguire2: /* Fall 2015 Semester */</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:''' Van Vleck B119<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_08 ''Chevallay Groups'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 15<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_15 ''The Important Questions'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 22<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 29 <br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 06<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 13<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 20<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~zcharles/ Zachary Charles]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 27<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 10<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 24<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 1<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 8<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 15<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=10184NTSGrad2015-09-11T20:19:30Z<p>Mmaguire2: /* Fall 2015 Semester */</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:''' Van Vleck B119<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_08 ''Chevallay Groups'']<br />
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|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=10183NTSGrad2015-09-11T20:19:03Z<p>Mmaguire2: /* Fall 2015 Semester */</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:''' Van Vleck B119<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_08 ''Chevallay Groupd'']<br />
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|-<br />
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| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=10182NTSGrad2015-09-11T20:17:27Z<p>Mmaguire2: /* Fall 2015 Semester */</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:''' Van Vleck B119<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2015 Semester =<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" | Sep 08<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sotirov/ Vladimir Sotirov]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_08 "Untitled"]<br />
|- <br />
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|-<br />
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|- <br />
| bgcolor="#E0E0E0" align="center" | <br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
[http://www.math.wisc.edu/~srostami/ Sean Rostami]<br />
<br />
----<br />
The seminar webpage for last semester, Spring 2014, is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=10181NTSGrad Fall 2015/Abstracts2015-09-11T20:14:59Z<p>Mmaguire2: </p>
<hr />
<div>== Sep 08 ==<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%" | '''Vladimir Sotirov'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Untitled''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
This is a prep talk for Sean Rostami's talk on September 10. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Infintely many supersingular primes for every elliptic curve over the rationals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Alternate Discriminants and Mass Formulas for Number Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Moments of prime polynomials in short intervals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Trouble with Sharblies''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Brandon Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''Yueke Hu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Mass equidistribution on modular curve of level N''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It was shown in previous works that the measure associated to holomorphic newforms of weight k and level q will tend weakly to the Haar measure on modular curve of level 1, as qk goes to infinity. In this talk I will show that this phenomenon is also true on modular curves of general level N.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Intro to Complex Dynamics''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Given a polynomial f(z) with complex coefficients, we can ask for which complex numbers p is the set {f(p), f(f(p)), f(f(f(p))),...} bounded, that is to ask which complex numbers have bounded forward orbit under f(z)? Alternatively we can turn the question around and ask for a fixed complex number p, for which (complex) polynomials is the forward orbit of p bounded? Finite? Periodic? These questions give the interesting fractal pictures many of you have probably seen. Amazingly many of the tools needed to approach these questions, arose well before computers allowed us to generate images like the one above. In this talk we will explore some of the basic tools and results of complex dynamics paying particular attention relations to number theory. The goal being to present some of the background material need for Laura DeMarco’s talk later in the week. (Also getting to see a really cool area of mathematics!)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''Ryan Julian'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''What is a K3 surface, and why are K1 and K2 surfaces only studied by mountain climbers?''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In preparation for Thursday's talk on the Shafarevich conjecture for K3 surfaces, I will attempt to build up enough of the definitions and background theory of differential geometry to define what a K3 surface is. In particular, I hope to explain how K3 surfaces fit into a larger classification of algebraic surfaces, allowing us to prove theorems in a more restricted setting before tackling surfaces of general type. Time permitting, I might even give a couple examples of K3 surfaces. If we're really lucky, I might even have time to explain the hilarious semi-joke in the title above.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''Jiuya Wang'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Parametrization of Cubic Field<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The discriminant parametrizes quadratic number fields well, but it will not<br />
work for cubic number fields. In order to develop a parametrization of<br />
cubic number fields, we will introduce the correspondence between a cubic<br />
ring with basis and a binary cubic form. The fact that there is a nice<br />
correspondence between orbits under <math>GL_2(\mathbb{Z})</math>-action will give the<br />
parametrization of cubic fields.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Organizer contact information ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=9544NTSGrad2015-03-20T21:42:52Z<p>Mmaguire2: /* Spring 2015 Semester */</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:''' Van Vleck B113<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2015 Semester =<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" | Jan 27<br />
| bgcolor="#F0B0B0" align="center" | Megan Maguire<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~yhu/ Yueke Hu]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 10<br />
| bgcolor="#F0B0B0" align="center" | William Cocke<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 17<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 10<br />
| bgcolor="#F0B0B0" align="center" | Dongxi Ye<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 7<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 14<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~steinberg/ Jason Steinberg]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 21<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 28<br />
| bgcolor="#F0B0B0" align="center" | Peng Yu<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 5<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
----<br />
The seminar webpage for Spring 2014 is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=9516NTSGrad2015-03-15T19:10:37Z<p>Mmaguire2: /* Spring 2015 Semester */</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:''' Van Vleck B113<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2015 Semester =<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" | Jan 27<br />
| bgcolor="#F0B0B0" align="center" | Megan Maguire<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~yhu/ Yueke Hu]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 10<br />
| bgcolor="#F0B0B0" align="center" | William Cocke<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 17<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 10<br />
| bgcolor="#F0B0B0" align="center" | Dongxi Ye<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 17<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 7<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 14<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~steinberg/ Jason Steinberg]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 21<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 28<br />
| bgcolor="#F0B0B0" align="center" | Peng Yu<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 5<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
----<br />
The seminar webpage for Spring 2014 is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=9160NTSGrad2015-01-21T15:43:33Z<p>Mmaguire2: /* Spring 2015 Semester */</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:''' Van Vleck B105<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Spring 2015 Semester =<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" | Jan 27<br />
| bgcolor="#F0B0B0" align="center" | Megan Maguire<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~yhu/ Yueke Hu]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 10<br />
| bgcolor="#F0B0B0" align="center" | William Cocke<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 17<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Feb 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 3<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~sparenti/ Solly Parenti]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 10<br />
| bgcolor="#F0B0B0" align="center" | Dongxi Ye<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Mar 17<br />
| bgcolor="#F0B0B0" align="center" | Peng Yu<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Mar 24<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 7<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 14<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~steinberg/ Jason Steinberg]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Apr 21<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~ross/ Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Apr 28<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | May 5<br />
| bgcolor="#F0B0B0" align="center" | <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
----<br />
The seminar webpage for Spring 2014 is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8711NTSGrad Fall 2015/Abstracts2014-11-03T20:11:04Z<p>Mmaguire2: /* Nov 04 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Infintely many supersingular primes for every elliptic curve over the rationals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Alternate Discriminants and Mass Formulas for Number Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Moments of prime polynomials in short intervals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Trouble with Sharblies''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Brandon Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''Yueke Hu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Mass equidistribution on modular curve of level N''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It was shown in previous works that the measure associated to holomorphic newforms of weight k and level q will tend weakly to the Haar measure on modular curve of level 1, as qk goes to infinity. In this talk I will show that this phenomenon is also true on modular curves of general level N.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Intro to Complex Dynamics''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Given a polynomial f(z) with complex coefficients, we can ask for which complex numbers p is the set {f(p), f(f(p)), f(f(f(p))),...} bounded, that is to ask which complex numbers have bounded forward orbit under f(z)? Alternatively we can turn the question around and ask for a fixed complex number p, for which (complex) polynomials is the forward orbit of p bounded? Finite? Periodic? These questions give the interesting fractal pictures many of you have probably seen. Amazingly many of the tools needed to approach these questions, arose well before computers allowed us to generate images like the one above. In this talk we will explore some of the basic tools and results of complex dynamics paying particular attention relations to number theory. The goal being to present some of the background material need for Laura DeMarco’s talk later in the week. (Also getting to see a really cool area of mathematics!)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Modular forms for definite quaternion algebras''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8710NTSGrad Fall 2015/Abstracts2014-11-03T20:10:53Z<p>Mmaguire2: /* Oct 28 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Infintely many supersingular primes for every elliptic curve over the rationals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Alternate Discriminants and Mass Formulas for Number Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Moments of prime polynomials in short intervals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Trouble with Sharblies''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Brandon Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''Yueke Hu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Mass equidistribution on modular curve of level N''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It was shown in previous works that the measure associated to holomorphic newforms of weight k and level q will tend weakly to the Haar measure on modular curve of level 1, as qk goes to infinity. In this talk I will show that this phenomenon is also true on modular curves of general level N.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Intro to Complex Dynamics''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Given a polynomial f(z) with complex coefficients, we can ask for which complex numbers p is the set {f(p), f(f(p)), f(f(f(p))),...} bounded, that is to ask which complex numbers have bounded forward orbit under f(z)? Alternatively we can turn the question around and ask for a fixed complex number p, for which (complex) polynomials is the forward orbit of p bounded? Finite? Periodic? These questions give the interesting fractal pictures many of you have probably seen. Amazingly many of the tools needed to approach these questions, arose well before computers allowed us to generate images like the one above. In this talk we will explore some of the basic tools and results of complex dynamics paying particular attention relations to number theory. The goal being to present some of the background material need for Laura DeMarco’s talk later in the week. (Also getting to see a really cool area of mathematics!)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Modular forms for definite quaternion algebras<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8709NTSGrad Fall 2015/Abstracts2014-11-03T20:10:39Z<p>Mmaguire2: /* Oct 07 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Infintely many supersingular primes for every elliptic curve over the rationals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Alternate Discriminants and Mass Formulas for Number Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Moments of prime polynomials in short intervals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''The Trouble with Sharblies''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Brandon Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''Yueke Hu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Mass equidistribution on modular curve of level N''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It was shown in previous works that the measure associated to holomorphic newforms of weight k and level q will tend weakly to the Haar measure on modular curve of level 1, as qk goes to infinity. In this talk I will show that this phenomenon is also true on modular curves of general level N.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intro to Complex Dynamics<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Given a polynomial f(z) with complex coefficients, we can ask for which complex numbers p is the set {f(p), f(f(p)), f(f(f(p))),...} bounded, that is to ask which complex numbers have bounded forward orbit under f(z)? Alternatively we can turn the question around and ask for a fixed complex number p, for which (complex) polynomials is the forward orbit of p bounded? Finite? Periodic? These questions give the interesting fractal pictures many of you have probably seen. Amazingly many of the tools needed to approach these questions, arose well before computers allowed us to generate images like the one above. In this talk we will explore some of the basic tools and results of complex dynamics paying particular attention relations to number theory. The goal being to present some of the background material need for Laura DeMarco’s talk later in the week. (Also getting to see a really cool area of mathematics!)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Modular forms for definite quaternion algebras<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8708NTSGrad Fall 2015/Abstracts2014-11-03T20:10:28Z<p>Mmaguire2: /* Sep 23 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Infintely many supersingular primes for every elliptic curve over the rationals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Alternate Discriminants and Mass Formulas for Number Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Moments of prime polynomials in short intervals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Trouble with Sharblies<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Brandon Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''Yueke Hu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Mass equidistribution on modular curve of level N''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It was shown in previous works that the measure associated to holomorphic newforms of weight k and level q will tend weakly to the Haar measure on modular curve of level 1, as qk goes to infinity. In this talk I will show that this phenomenon is also true on modular curves of general level N.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intro to Complex Dynamics<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Given a polynomial f(z) with complex coefficients, we can ask for which complex numbers p is the set {f(p), f(f(p)), f(f(f(p))),...} bounded, that is to ask which complex numbers have bounded forward orbit under f(z)? Alternatively we can turn the question around and ask for a fixed complex number p, for which (complex) polynomials is the forward orbit of p bounded? Finite? Periodic? These questions give the interesting fractal pictures many of you have probably seen. Amazingly many of the tools needed to approach these questions, arose well before computers allowed us to generate images like the one above. In this talk we will explore some of the basic tools and results of complex dynamics paying particular attention relations to number theory. The goal being to present some of the background material need for Laura DeMarco’s talk later in the week. (Also getting to see a really cool area of mathematics!)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Modular forms for definite quaternion algebras<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8707NTSGrad Fall 2015/Abstracts2014-11-03T20:10:16Z<p>Mmaguire2: /* Sep 16 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Infintely many supersingular primes for every elliptic curve over the rationals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Alternate Discriminants and Mass Formulas for Number Fields''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Moments of prime polynomials in short intervals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Trouble with Sharblies<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Brandon Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''Yueke Hu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Mass equidistribution on modular curve of level N''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It was shown in previous works that the measure associated to holomorphic newforms of weight k and level q will tend weakly to the Haar measure on modular curve of level 1, as qk goes to infinity. In this talk I will show that this phenomenon is also true on modular curves of general level N.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intro to Complex Dynamics<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Given a polynomial f(z) with complex coefficients, we can ask for which complex numbers p is the set {f(p), f(f(p)), f(f(f(p))),...} bounded, that is to ask which complex numbers have bounded forward orbit under f(z)? Alternatively we can turn the question around and ask for a fixed complex number p, for which (complex) polynomials is the forward orbit of p bounded? Finite? Periodic? These questions give the interesting fractal pictures many of you have probably seen. Amazingly many of the tools needed to approach these questions, arose well before computers allowed us to generate images like the one above. In this talk we will explore some of the basic tools and results of complex dynamics paying particular attention relations to number theory. The goal being to present some of the background material need for Laura DeMarco’s talk later in the week. (Also getting to see a really cool area of mathematics!)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Modular forms for definite quaternion algebras<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8706NTSGrad Fall 2015/Abstracts2014-11-03T20:10:06Z<p>Mmaguire2: /* Sep 09 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Infintely many supersingular primes for every elliptic curve over the rationals''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Alternate Discriminants and Mass Formulas for Number Fields<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Moments of prime polynomials in short intervals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Trouble with Sharblies<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Brandon Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''Yueke Hu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Mass equidistribution on modular curve of level N''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It was shown in previous works that the measure associated to holomorphic newforms of weight k and level q will tend weakly to the Haar measure on modular curve of level 1, as qk goes to infinity. In this talk I will show that this phenomenon is also true on modular curves of general level N.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intro to Complex Dynamics<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Given a polynomial f(z) with complex coefficients, we can ask for which complex numbers p is the set {f(p), f(f(p)), f(f(f(p))),...} bounded, that is to ask which complex numbers have bounded forward orbit under f(z)? Alternatively we can turn the question around and ask for a fixed complex number p, for which (complex) polynomials is the forward orbit of p bounded? Finite? Periodic? These questions give the interesting fractal pictures many of you have probably seen. Amazingly many of the tools needed to approach these questions, arose well before computers allowed us to generate images like the one above. In this talk we will explore some of the basic tools and results of complex dynamics paying particular attention relations to number theory. The goal being to present some of the background material need for Laura DeMarco’s talk later in the week. (Also getting to see a really cool area of mathematics!)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Modular forms for definite quaternion algebras<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8705NTSGrad Fall 2015/Abstracts2014-11-03T20:09:21Z<p>Mmaguire2: /* Nov 04 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Infintely many supersingular primes for every elliptic curve over the rationals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Alternate Discriminants and Mass Formulas for Number Fields<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Moments of prime polynomials in short intervals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Trouble with Sharblies<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Brandon Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''Yueke Hu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Mass equidistribution on modular curve of level N''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It was shown in previous works that the measure associated to holomorphic newforms of weight k and level q will tend weakly to the Haar measure on modular curve of level 1, as qk goes to infinity. In this talk I will show that this phenomenon is also true on modular curves of general level N.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intro to Complex Dynamics<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Given a polynomial f(z) with complex coefficients, we can ask for which complex numbers p is the set {f(p), f(f(p)), f(f(f(p))),...} bounded, that is to ask which complex numbers have bounded forward orbit under f(z)? Alternatively we can turn the question around and ask for a fixed complex number p, for which (complex) polynomials is the forward orbit of p bounded? Finite? Periodic? These questions give the interesting fractal pictures many of you have probably seen. Amazingly many of the tools needed to approach these questions, arose well before computers allowed us to generate images like the one above. In this talk we will explore some of the basic tools and results of complex dynamics paying particular attention relations to number theory. The goal being to present some of the background material need for Laura DeMarco’s talk later in the week. (Also getting to see a really cool area of mathematics!)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''Vlad Matei'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Modular forms for definite quaternion algebras<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Jacquet-Langlands theorem states that given two quaternion algebras, then certain automorphic forms for one of them are in canonical bijection with certain automorphic forms for the other. This seems far too general and also a bit vague.So if one translates the statement of the JL theorem down a bit, we should have that certain classical modular forms should be related to certain "modular forms" on other quaternion algebras. We will define modular forms for quaternion algebras, and we will see that for definite quaternion algebras they are very concrete algebraic objects.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8704NTSGrad Fall 2015/Abstracts2014-11-03T20:08:19Z<p>Mmaguire2: /* Oct 28 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Infintely many supersingular primes for every elliptic curve over the rationals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Alternate Discriminants and Mass Formulas for Number Fields<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Moments of prime polynomials in short intervals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Trouble with Sharblies<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Brandon Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''Yueke Hu'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Mass equidistribution on modular curve of level N''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
It was shown in previous works that the measure associated to holomorphic newforms of weight k and level q will tend weakly to the Haar measure on modular curve of level 1, as qk goes to infinity. In this talk I will show that this phenomenon is also true on modular curves of general level N.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''David Bruce'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Intro to Complex Dynamics<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Given a polynomial f(z) with complex coefficients, we can ask for which complex numbers p is the set {f(p), f(f(p)), f(f(f(p))),...} bounded, that is to ask which complex numbers have bounded forward orbit under f(z)? Alternatively we can turn the question around and ask for a fixed complex number p, for which (complex) polynomials is the forward orbit of p bounded? Finite? Periodic? These questions give the interesting fractal pictures many of you have probably seen. Amazingly many of the tools needed to approach these questions, arose well before computers allowed us to generate images like the one above. In this talk we will explore some of the basic tools and results of complex dynamics paying particular attention relations to number theory. The goal being to present some of the background material need for Laura DeMarco’s talk later in the week. (Also getting to see a really cool area of mathematics!)<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=8703NTSGrad2014-11-03T20:07:41Z<p>Mmaguire2: /* Fall 2014 Semester */</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:''' Van Vleck B105<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2014 Semester =<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'''<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Aug 26<br />
| bgcolor="#F0B0B0" align="center" | (Summer)<br />
| bgcolor="#BCE2FE" align="center" | (Summer)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 02<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jain/ Lalit Jain] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_02 ''Monodromy computations in topology and number theory'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 09<br />
| bgcolor="#F0B0B0" align="center"| Megan Maguire<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_09 ''Infinitely many supersingular primes for every elliptic curve over the rationals'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 16<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~sjohnson/ Silas Johnson]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_16 ''Alternate Discriminants and Mass Formulas for Number Fields'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 23<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_23 ''Moments of prime polynomials in short intervals'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 30<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 07<br />
| bgcolor="#F0B0B0" align="center"| Wil Cocke<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_07 ''The Trouble with Sharblies'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 14<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 21<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~yhu/ Yueke Hu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_21 ''Mass equidistribution on modular curve of level N'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 28<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_28 ''Intro to Complex Dynamics'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 04<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_04 ''Modular forms for definite quaternion algebras'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 11<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 18<br />
| bgcolor="#F0B0B0" align="center"| Peng Yu<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 25<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 02<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~ross Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 09<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== 2015 ==<br />
<br />
The seminar webpage for NTS Spring 2015 is [[NTS_Spring_2015|here]].<br><br />
The abstract webpage for NTS Spring 2015 Abstracts is [[NTS_Spring_2015_Abstract|here]]<br><br><br />
The seminar webpage for NTS Grad Spring 2015 is [[NTS_Grad_Spring_2015|here]].<br><br />
The abstract webpage for NTS Grad Spring 2015 Abstracts is [[NTS_Grad_Spring_2015_Abstract|here]]<br />
<br />
==Creating a new BLANK NTS seminar page==<br />
<br />
This is a link to a blank NTS page for creating new ones. It's empty. Copy and paste the code to any new NTS schedule page you need. [[NTS_NEW]]<br><br />
This is a link to a blank NTS abstract page for creating new ones. It's empty. Copy and paste the code to any new NTS abstract page you need.[[NTS_ABSTRACT_NEW]]<br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
----<br />
The seminar webpage for Spring 2014 is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=8702NTSGrad2014-11-03T20:07:09Z<p>Mmaguire2: /* Fall 2014 Semester */</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:''' Van Vleck B105<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2014 Semester =<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'''<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Aug 26<br />
| bgcolor="#F0B0B0" align="center" | (Summer)<br />
| bgcolor="#BCE2FE" align="center" | (Summer)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 02<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jain/ Lalit Jain] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_02 ''Monodromy computations in topology and number theory'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 09<br />
| bgcolor="#F0B0B0" align="center"| Megan Maguire<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_09 ''Infinitely many supersingular primes for every elliptic curve over the rationals'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 16<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~sjohnson/ Silas Johnson]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_16 ''Alternate Discriminants and Mass Formulas for Number Fields'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 23<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_23 ''Moments of prime polynomials in short intervals'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 30<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 07<br />
| bgcolor="#F0B0B0" align="center"| Wil Cocke<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_07 ''The Trouble with Sharblies'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 14<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 21<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~yhu/ Yueke Hu]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_21 ''Mass equidistribution on modular curve of level N'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 28<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_28 ''Intro to Complex Dynamics'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 04<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Nov_04 "Modular forms for definite quaternion algebras"]<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 11<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 18<br />
| bgcolor="#F0B0B0" align="center"| Peng Yu<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 25<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 02<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~ross Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 09<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== 2015 ==<br />
<br />
The seminar webpage for NTS Spring 2015 is [[NTS_Spring_2015|here]].<br><br />
The abstract webpage for NTS Spring 2015 Abstracts is [[NTS_Spring_2015_Abstract|here]]<br><br><br />
The seminar webpage for NTS Grad Spring 2015 is [[NTS_Grad_Spring_2015|here]].<br><br />
The abstract webpage for NTS Grad Spring 2015 Abstracts is [[NTS_Grad_Spring_2015_Abstract|here]]<br />
<br />
==Creating a new BLANK NTS seminar page==<br />
<br />
This is a link to a blank NTS page for creating new ones. It's empty. Copy and paste the code to any new NTS schedule page you need. [[NTS_NEW]]<br><br />
This is a link to a blank NTS abstract page for creating new ones. It's empty. Copy and paste the code to any new NTS abstract page you need.[[NTS_ABSTRACT_NEW]]<br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
----<br />
The seminar webpage for Spring 2014 is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8507NTSGrad Fall 2015/Abstracts2014-10-06T19:11:23Z<p>Mmaguire2: /* Oct 14 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Infintely many supersingular primes for every elliptic curve over the rationals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Alternate Discriminants and Mass Formulas for Number Fields<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Moments of prime polynomials in short intervals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Trouble with Sharblies<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Brandon Alberts'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8506NTSGrad Fall 2015/Abstracts2014-10-06T19:10:55Z<p>Mmaguire2: /* Oct 07 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Infintely many supersingular primes for every elliptic curve over the rationals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Alternate Discriminants and Mass Formulas for Number Fields<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Moments of prime polynomials in short intervals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Trouble with Sharblies<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Trouble with Sharblies<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8505NTSGrad Fall 2015/Abstracts2014-10-06T19:10:13Z<p>Mmaguire2: /* Oct 14 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Infintely many supersingular primes for every elliptic curve over the rationals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Alternate Discriminants and Mass Formulas for Number Fields<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Moments of prime polynomials in short intervals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''Will Cocke'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | The Trouble with Sharblies<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The Sharbly complex provides a generalization of modular symbols and can be used to compute the Hecke eigenvalues on arithmetic cohomology. Such eigenvalues provide useful information pertaining to generalizations of Serre's conjecture. I will introduce the Sharbly complex and examine the necessary reduction techniques needed to compute the Hecke action. A friendly introduction to a new and emerging tool in computational number theory.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 09 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
<br />
== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=8504NTSGrad2014-10-06T19:07:15Z<p>Mmaguire2: /* Fall 2014 Semester */</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:''' Van Vleck B105<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2014 Semester =<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'''<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Aug 26<br />
| bgcolor="#F0B0B0" align="center" | (Summer)<br />
| bgcolor="#BCE2FE" align="center" | (Summer)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 02<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jain/ Lalit Jain] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_02 ''Monodromy computations in topology and number theory'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 09<br />
| bgcolor="#F0B0B0" align="center"| Megan Maguire<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_09 ''Infinitely many supersingular primes for every elliptic curve over the rationals'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 16<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~sjohnson/ Silas Johnson]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_16 ''Alternate Discriminants and Mass Formulas for Number Fields'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 23<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_23 ''Moments of prime polynomials in short intervals'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 30<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 07<br />
| bgcolor="#F0B0B0" align="center"| Wil Cocke<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Oct_07 ''The Trouble with Sharblies'']<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 14<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 21<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~yhu/ Yueke Hu]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 28<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 04<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 11<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 18<br />
| bgcolor="#F0B0B0" align="center"| Peng Yu<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 25<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 02<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~ross Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 09<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
----<br />
The seminar webpage for Spring 2014 is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=8370NTSGrad2014-09-23T16:50:04Z<p>Mmaguire2: /* Fall 2014 Semester */</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:''' Van Vleck B105<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2014 Semester =<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'''<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Aug 26<br />
| bgcolor="#F0B0B0" align="center" | (Summer)<br />
| bgcolor="#BCE2FE" align="center" | (Summer)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 02<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jain/ Lalit Jain] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_02 ''Monodromy computations in topology and number theory'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 09<br />
| bgcolor="#F0B0B0" align="center"| Megan Maguire<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_09 ''Infinitely many supersingular primes for every elliptic curve over the rationals'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 16<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~sjohnson/ Silas Johnson]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_16 ''Alternate Discriminants and Mass Formulas for Number Fields'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 23<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_23 ''Moments of prime polynomials in short intervals'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 30<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 07<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 14<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 21<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 28<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 04<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 11<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 18<br />
| bgcolor="#F0B0B0" align="center"| Peng Yu<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 25<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 02<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~ross Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 09<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
----<br />
The seminar webpage for Spring 2014 is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad_Fall_2015/Abstracts&diff=8369NTSGrad Fall 2015/Abstracts2014-09-23T16:48:52Z<p>Mmaguire2: /* Sep 23 */</p>
<hr />
<div>== Sep 02 ==<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%" | '''Lalit Jain'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | ''Monodromy computations in topology and number theory''<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, explain some number theoretic applications, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. <br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 09 ==<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%" | '''Megan Maguire'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Infintely many supersingular primes for every elliptic curve over the rationals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
In his 1987 Inventiones paper, Dr. Noam Elkies proved that every elliptic curve over <math>\mathbb{Q}</math> has infinitely many supersingular primes. We shall discuss some of the mathematics needed to prove this result and give a proof.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Silas Johnson'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Alternate Discriminants and Mass Formulas for Number Fields<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
Kedlaya and Wood have explored alternate invariants for number fields, with the idea of replacing the discriminant in standard field-counting questions with one of these alternate invariants. We further explore the space of “reasonable” invariants, expanding on Kedlaya and Wood’s definition. We also discuss a theorem on mass formulas for these invariants.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 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%" | '''Daniel Hast'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | Moments of prime polynomials in short intervals.<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
How many prime numbers occur in a typical "short interval" of fixed width, and how are primes distributed among such intervals? We examine the analogue of this problem for polynomials over a finite field. Our approach is geometric: we interpret each moment of the distribution in terms of counting certain points on an algebraic variety, and we use an algebraic analogue of the Lefschetz fixed-point theorem to compute the leading terms of this "twisted" point-count. As a motivating example, we realize the "prime polynomial theorem" as a geometric statement.<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Sep 30 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 07 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 14 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 21 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Oct 28 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 04 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 11 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 18 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Nov 25 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
| bgcolor="#BCD2EE" | <br />
ABSTRACT<br />
|} <br />
</center><br />
<br />
<br><br />
<br />
== Dec 02 ==<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
|-<br />
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ABSTRACT<br />
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<br><br />
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== Dec 09 ==<br />
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<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%" | '''SPEAKER'''<br />
|-<br />
| bgcolor="#BCD2EE" align="center" | TITLE<br />
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ABSTRACT<br />
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== Organizer contact information ==<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
<br><br />
<br />
----<br />
Return to the [[NTSGrad|Number Theory Graduate Student Seminar Page]]<br />
<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2https://wiki.math.wisc.edu/index.php?title=NTSGrad&diff=8292NTSGrad2014-09-16T01:36:16Z<p>Mmaguire2: /* Fall 2014 Semester */</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:''' Van Vleck B105<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|Number Theory Seminar]] talk on the following Thursday.<br />
These talks should be aimed at beginning graduate students, and should try to <br />
explain some of the background, terminology, and ideas for the Thursday talk.<br />
<br />
= Fall 2014 Semester =<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'''<br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Aug 26<br />
| bgcolor="#F0B0B0" align="center" | (Summer)<br />
| bgcolor="#BCE2FE" align="center" | (Summer)<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 02<br />
| bgcolor="#F0B0B0" align="center" | [http://www.math.wisc.edu/~jain/ Lalit Jain] <br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_02 ''Monodromy computations in topology and number theory'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 09<br />
| bgcolor="#F0B0B0" align="center"| Megan Maguire<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_09 ''Infinitely many supersingular primes for every elliptic curve over the rationals'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 16<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~sjohnson/ Silas Johnson]<br />
| bgcolor="#BCE2FE"| [https://www.math.wisc.edu/wiki/index.php/NTSGrad/Abstracts#Sep_16 ''Alternate Discriminants and Mass Formulas for Number Fields'']<br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 23<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~hast/ Daniel Hast]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Sep 30<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 07<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Oct 14<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~blalberts/ Brandon Alberts]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 21<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Oct 28<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~djbruce/ David Bruce]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 04<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~mvlad/ Vlad Matei]<br />
| bgcolor="#BCE2FE"| <br />
|-<br />
| bgcolor="#E0E0E0" align="center" | Nov 11<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~mrjulian/ Ryan Julian]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 18<br />
| bgcolor="#F0B0B0" align="center"| Peng Yu<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Nov 25<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 02<br />
| bgcolor="#F0B0B0" align="center"| [http://www.math.wisc.edu/~ross Daniel Ross]<br />
| bgcolor="#BCE2FE"| <br />
|- <br />
| bgcolor="#E0E0E0" align="center" | Dec 09<br />
| bgcolor="#F0B0B0" align="center"| <br />
| bgcolor="#BCE2FE"| <br />
|}<br />
<br />
</center><br />
<br />
<br><br />
<br />
== Organizers ==<br />
<br />
Megan Maguire (mmaguire2@math.wisc.edu)<br />
<br />
Ryan Julian (mrjulian@math.wisc.edu)<br />
<br />
Sean Rostami (srostami@math.wisc.edu)<br />
<br />
----<br />
The seminar webpage for Spring 2014 is [[NTSGrad_Spring_2014|here]].<br><br />
----<br />
Return to the [[NTS|Number Theory Seminar Page]]<br />
<br />
Return to the [[Algebra|Algebra Group Page]]</div>Mmaguire2