Time: Thursday, Apirl 11th, 2024 , 14:00-15:00
Abstract: In this talk, we will first give a brief introduction to elliptic mod- ular forms (i.e., degree 1 case). Then we will focus on reporting some recent results on the classical Siegel modular forms of degree 2 and representation theory of the symplectic similitude group GSp(4) based on my own work and those with my collaborators. In particular, we will describe how to use local-global representation theory of GSp(4) and the classification of the as- sociated Arthur packets to obtain new dimension formulas of certain family of Siegel modular forms of degree 2, and also sketch how to use the the- ory of L-functions to give several refined strong multiplicity one results for paramodular newforms. Finally, we will also briefly discuss some applications of these results to other related topics in number theory.
Note that there will be a short pretalk on introduction to the represen- tation theory of the p-adic group GSp(4).