NTSGrad Fall 2022/Abstracts

This page contains the titles and abstracts for talks scheduled in the Spring 2022 semester. To go back to the main GNTS page, click here.

9/13

Ivan Aidun

A Case Study in the Analogy Between Z and F_q[t]

An influential concept in modern number theory is the idea that the integers Z and the ring of polynomials over a finite field F_q[t] share many traits.  In this talk, I will discuss some particular examples of how this analogy can work, focusing on zeta functions and counting problems.  No prior familiarity will be required!

9/20

Jiaqi Hou

Poincare series and Petersson trace formula

I will talk about the Poincare series, which are basic examples of modular forms, and the Petersson trace formula for SL(2,Z). Then I will discuss some applications of Petersson's formula.

9/27

No speaker

10/4

Eiki Norizuki

p-adic L-functions

In this talk, I will look at how p-adic L-functions are constructed as first demonstrated by Kubota and Leopoldt. These are p-adic analogues of the Dirichlet L-functions and the main idea of the construction comes from interpolating the negative integer values of the classical L-functions. This talk should be accessible to everyone.

10/11

Sun Woo Park

Rank 2 local systems and Elliptic Curves

We'll understand some key properties of elliptic curves (Weil Pairing, eigenvalues of Frobenius, and poles of j-invariants) and try to see how these properties are closely tied in with understanding certain properties of rank 2 local systems over an open subset of the projective line $\mathbb{P}^1$.This is a preparation talk for the NTS talk on Thursday.

10/18

John Yin

Some Examples in Etale Cohomology

I will motivate, define, and give explicit examples of etale cohomology. In addition, I will compute the Galois action on etale cohomology in certain cases.

10/25

TBA

TBA

11/1

TBA

TBA

11/8

TBA

TBA

11/15

TBA

TBA

11/22

TBA

TBA

11/29

TBA

TBA

12/6

TBA

TBA

12/13

TBA

TBA