NTSGrad Spring 2022/Abstracts: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
(Created page with "This page contains the titles and abstracts for talks scheduled in the Fall 2021 semester. To go back to the main GNTS page, click here. == Sep 14 ==...")
 
No edit summary
Line 2: Line 2:




== Sep 14 ==
== Jan 25 ==


<center>
<center>
Line 17: Line 17:
<br>
<br>


== Sep 21 ==
== Feb 1 ==


<center>
<center>
Line 32: Line 32:
<br>
<br>


== Sep 28 ==
== Feb 8 ==


<center>
<center>
Line 51: Line 51:
<br>
<br>


== Oct 5 ==
== Feb 15 ==


<center>
<center>
Line 66: Line 66:
<br>
<br>


== Oct 12 ==
== Feb 25 ==


<center>
<center>
Line 81: Line 81:
<br>
<br>


== Oct 19 ==
== Mar 1 ==


<center>
<center>
Line 96: Line 96:
<br>
<br>


== Oct 26 ==
== Mar 8 ==


<center>
<center>
Line 111: Line 111:
<br>
<br>


== Nov 2 ==
== Mar 15 ==


<center>
<center>
Line 127: Line 127:
<br>
<br>


== Nov 9 ==
== Mar 22 ==


<center>
<center>
Line 142: Line 142:
<br>
<br>


== Nov 16 ==
== Mar 29 ==


<center>
<center>
Line 158: Line 158:


<br>
<br>
== Nov 23 ==
 
== Apr 5 ==


<center>
<center>
Line 178: Line 179:
<br>
<br>


== Nov 30 ==
== Apr 12 ==


<center>
<center>
Line 196: Line 197:
<br>
<br>


== Dec 7==
== Apr 19 ==


<center>
<center>
Line 213: Line 214:
<br>
<br>


== Dec 14 ==
== Apr 26 ==
 
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''John Yin'''
|-
| bgcolor="#BCD2EE"  align="center" | ''Heights on Stacks''
|-
| bgcolor="#BCD2EE"  |  I will motivate and introduce the definition of a height. Then, I will talk a bit about Arakelov height. This will then lead into a recent paper by Ellenberg, Satriano, and Zureick-Brown, which introduces a notion of height on stacks.
 
 
 
 
 
|}                                                                       
</center>
 
<br>
 
== May 3 ==


<center>
<center>

Revision as of 02:26, 24 January 2022

This page contains the titles and abstracts for talks scheduled in the Fall 2021 semester. To go back to the main GNTS page, click here.


Jan 25

Hyun Jong Kim
What would Jordan do?
In his notes for students, Jordan has a list of general topics and references in number theory/algebraic geometry/arithmetic geometry that students in arithmetic geometry should be comfortable with after a certain point of time. I will introduce some language used in these general topics for beginners.


Feb 1

Peter YI WEI
The S-Unit equation: p-adic approaches
In this talk, I will go over the history of rational/integral points on curves. In particular, I will introduce a recent proof of the S-unit equation using p-adic period maps, given by Lawrence-Venkatesh.


Feb 8

TBA
TBA


|}


Feb 15

Yifan Wei
Lifting a smooth curve from char p to char 0
Geometry over char p is fascinating or frustrating, depending on who you are. However varieties over char 0 could be enjoyed by geometers of all kinds. We will dicuss one way of lifting a smooth projective variety from char p to char 0. After applying our technique to curves we briefly mention the situation in higher dimensions. And if time permits, we discuss a non-liftable example by Serre.


Feb 25

TBA
TBA


Mar 1

TBA
TBA


Mar 8

Di Chen
Special values of zeta functions at positive even integers
I will introduce Euler's classical result over Q, Klingen-Siegel theorem over totally real number fields, and Zagier's theorems and conjectures over general number fields. I will give many examples and discuss their proofs. If time permits, I will discuss its relation with K-theory.


Mar 15

Jerry Y. Fu
Diophantine approximation: How I learned to stop worrying and love integral points
Diophantine approximation is a crucial tool in studying integral points and Schlickewei's theorem is a very useful theorem in proving finiteness theorems on integral points. In the first part of my talk I will show some elegant proof as applications of the subspace theorem such as Vojta's theorem, the S-unit equation, and then I will introduce main conjectures: Vojta, Mordell, Bombieri and Lang, and their relations to each other.


Mar 22

TBA
TBA


Mar 29

TBA
TBA



Apr 5

Eiki Norizuki
Local Reciprocity

I will talk about local reciprocity, a correspondence of the Galois group of the maximal abelian extension and the multiplicative group. In particular, I will talk about Lubin-Tate theory which constructs this map.



Apr 12

Tejasi Bhatnagar
Counting Number fields: A baby example using Bhargava’s techniques.
In this talk, we will walk through a simple example of counting quadratic extensions using the discriminant. Although, this has been done using classical methods, we will highlight the techniques used by Bhargava through our example, that were essentially used to count the higher degree cases.



Apr 19

Qiao He
Siegel-Weil Formula
Given a positive definite quadratic form X_1^2+...+X_n^2, a natural question to ask is can we find a formula for $r_n(m)=\#\{X\in Z^n| Q(X)=m\}$. Although no explicit formula for $r_n(m)$ is known in general, there do exist an average formula, which is a prototype of the so called Siegel-Weil formula. In this talk, I will introduce Siegel-Weil formula, and show how Deuring's mass formula for supersingular elliptic curve and Hurwitz class number formula follows from Siegel-Weil formula.



Apr 26

John Yin
Heights on Stacks
I will motivate and introduce the definition of a height. Then, I will talk a bit about Arakelov height. This will then lead into a recent paper by Ellenberg, Satriano, and Zureick-Brown, which introduces a notion of height on stacks.




May 3

John Yin
Heights on Stacks
I will motivate and introduce the definition of a height. Then, I will talk a bit about Arakelov height. This will then lead into a recent paper by Ellenberg, Satriano, and Zureick-Brown, which introduces a notion of height on stacks.