NTSGrad Fall 2021/Abstracts

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

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.

Sep 21

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.

Sep 28

TBA

TBA

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Oct 5

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.

Oct 12

TBA

TBA

Oct 19

TBA

TBA

Oct 26

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.

Nov 2

TBA

TBA

Nov 9

TBA

TBA

Nov 16

TBA

TBA

Nov 23

TBA

TBA

Nov 30

TBA

TBA

Dec 7

TBA

TBA

Dec 14

TBA

TBA