NTSGrad Spring 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.

Jan 25

Jerry Yu Fu

Canonical lifting and isogeny classes of Abelian varieties over finite field

I will give a brief introduction from Serre-Tate's canonical lifting, the Grothendieck-Messing theory and their applications to class group and estimation of size of isogeny classes of certain type of abelian varieties over finite fields. I will present some recently proved results by me and some with my collaborator.

Feb 1

TBA

Feb 8

Di Chen

A non-trivial bound on 5-torsion in class groups.

I will discuss A. Shankar and J. Tsimerman’s recent work on a non-trivial bound on 5-torsion in class groups of imaginary quadratic fields. I focus on ideas of proofs and assume several black boxes without proofs. This is a good application of elliptic curves and Galois cohomology.

Feb 15

TBA

Feb 25

TBA

Mar 1

TBA

Mar 8

TBA

Mar 15

TBA

Mar 22

TBA

Mar 29

TBA

Apr 5

TBA

Apr 12

TBA

Apr 19

TBA

Apr 26

TBA

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

Jerry Yu Fu

Canonical lifting and size of isogeny classes

I will give a brief review from Serre-Tate's canonical lifting theorem, the Grothendieck-Messing theory and their applications to class group and isogeny classes of certain type of abelian varieties over finite fields. I will present some recently proved results by me and some with my collaborator.