NTSGrad Fall 2020/Abstracts
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.
|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.
|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.