Fall 2020

Due to the ongoing COVID-19 pandemic, the AGNT seminar will not be meeting regularly.

En lieu of the regular seminar, we encourage you to participate in the many related online-only seminars being run during this time:

Watch this space for occasional online-only events throughout the semester:

• September 19-20: PAJAMAS (PAlmetto Joint Arithmetic, Modularity, and Analysis Series)

• October 26 at 4:30: Tracy Huggins (UofSC) - Essential Dimension over the Rationals

Abstract: The essential dimension of an algebraic group is an interesting numerical invariant that ties together problems in representation theory, algebraic geometry, and number theory. The essential dimension of finite groups is especially relevant and work to classify finite groups of small essential dimension has been an ongoing project in the literature.

I present a conjectural classification of finite groups of essential dimension 2 over $\mathbb{Q}$ and the current state of progress on this problem.

(Zoom meeting details sent by department-wide email or contact Alex Duncan.)

• October 30 at 4:45: Shaoyun Yi (UofSC) - On counting cuspidal automorphic representations and an equidistribution theorem for GSp(4)

Abstract: There is a so-called vertical Sato-Tate conjecture for GL(2), which describes an equidistribution of Hecke eigenvalues of classical modular forms with respect to certain measure. In this talk, we will discuss a similar equidistribution result for a family of cuspidal automorphic representations of GSp(4). We formulate our theorem explicitly in terms of the number of cuspidal automorphic representations of GSp(4) satisfying certain conditions. To count the number of these cuspidal automorphic representations, we will explore the connection between Siegel cusp forms and cuspidal automorphic representations of GSp(4). This is a joint work with Manami Roy and Ralf Schmidt.

(Zoom meeting details sent by department-wide email or contact Alex Duncan.)