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May 7, 2021 (Friday), 11:00 am

Number Theory Seminar

Effective equidistribution of rational points on expanding horospheres

Min Lee, University of Bristol
Number Theory Seminar page for Zoom meeting information

Abstract: The main purpose of this talk is to provide an effective version of a result due to Einsiedler, Mozes, Shah and Shapira, on the equidistribution of primitive rational points on expanding horospheres in the space of unimodular lattices. Their proof uses techniques from homogeneous dynamics and relies in particular on measure-classification theorems due to Ratner. Instead, we pursue an alternative strategy based on spectral theory of automorphic forms, Fourier analysis and Weil’s bound for Kloosterman sums which yields an effective estimate on the rate of convergence in the space of (d+1)-dimensional Euclidean lattices.

This is a joint work with D. El-Baz, B. Huang and J. Marklof.

 

May 7, 2021 (Friday), 4:10 pm

Subfactor Seminar

The von Neumann Algebras from Cusp Forms Acting on Holomorphic Discrete Series

Jun Yang, Vanderbilt University,Subfactor Seminar page for Zoom meeting information

Given a Fuchsian group, its cusp forms intertwine its actions on the holomorphic discrete series representation of SL(2,R). We show these cusp forms can generate the entire commutant of its groups von Neumann algebra. We generalize this result to a semi-simple Lie group G with holomorphic discrete series and their lattices. We prove that the commutant is the tensor of its subalgebra from cusp forms and the endomorphism algebra of a highest weight representation V of a maximal compact subgroup of G. If the lattice is ICC, this gives a subfactor of type II_1 with index equals to of dim(V)^2.

May 10, 2021 (Monday), 1:00 pm

Qualifying Examination- Andrew Jarnevic

Zoom Link
https://vanderbilt.zoom.us/j/92523455948?pwd=eTZjWFR5KzRsQlFKN1NiemxuMXQ3UT09

May 11, 2021 (Tuesday), 1:00 pm

Qualifying Examination- Samuel Rizzo

Zoom ID is 996 8673 5898

May 12, 2021 (Wednesday), 11:00 am

Number Theory Seminar

Partition Eisenstein series and semi-modular forms

Matthew Just -University of Georgia
Number Theory Seminar page for Zoom meeting information

We identify a class of “semi-modular” forms invariant on special subgroups of GL2(Z), which includes classical modular forms together with complementary classes of functions that are also nice in a specific sense. We define an Eisenstein- like series summed over integer partitions, and use it to construct families of semi- modular forms. We ask whether other examples exist, and what properties they all share. This is joint work with Robert Schneider.

May 13, 2021 (Thursday), 9:00 am

Dissertation Defense- Wenhao Wang

Title: Dehn Functions of Metabelian Groups
vanderbilt.zoom.us/j/99524070585?pwd=NFFiYjJuUldhUmlOS1JPK1grOU10QT09
Meeting ID: 995 2407 0585
Passcode: 908697

May 28, 2021 (Friday), 4:10 pm

Subfactor Seminar

Talk Title TBA

Matthew Zaremsky, University of Albany, SUNY
Subfactor Seminar page for Zoom meeting information

June 1, 2021 (Tuesday), 1:45 pm

Defense of Jun Yang-The von Neumann Algebras from Cusp Forms Acting on Holomorphic Discrete Series

Join Zoom Meeting
https://vanderbilt.zoom.us/j/95565684431?pwd=QStuTGJnVlBkYzFCMnJmUC9xbnhkZz09
Meeting ID: 955 6568 4431
Passcode: 373230
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