NTSGrad Fall 2020/Abstracts

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This page contains the titles and abstracts for talks scheduled in the Fall 2020 semester. To go back to the main GNTS page, click here.


Sep 15

Qiao He
Local Arithmetic Siegel-Weil Formula at Ramified Prime
In this talk, I will describe a local arithmetic Siegel-Weil formula which relates certain intersection number on U(1,1) Rapoport-Zink space with local density. Via p-adic uniformization, this can be used to establish a global Siegel-Weil formula. The main novelty of this work is that we consider the ramified case. This is a joint work with Yousheng Shi and Tonghai Yang.


Sep 22

Johnny Han
Bounding Numbers Fields up to Discriminant

For those interested in arithmetic statistics, I'll present a quick proof of Schmidt's bound on numbers fields of given degree and bounded discriminant, as well as giving a quick overview of recent improvements on this bound by Ellenberg and Venkatesh.


Sep 29

Johnny Han
Dial M_{1,1} for moduli

We'll try to give a brief introduction to moduli problems, with an eye towards moduli of elliptic curves.