Organizer:Koji Shimizu (YMSC), Yihang Zhu (YMSC)
Time:Fri., 15:00-17:30, Sept. 27, 2024
Venue: Shuangqing C654 (note that the lecture room was changed)
15:00-16:00, Gerard van der Geer
Title: Picard modular forms and curves of genus three
Abstract: We discuss how to calculate traces of Hecke operators on Picard modular forms by the use of point counting of curves of genus three over finite fields. This is joint work with Jonas Bergstroem and Fabien Clery.
16:30-17:30, Yifeng Liu
Title: Bessel periods and Selmer groups over ordinary eigenvariety
Abstract: We (re)construct the ordinary part of the eigenvariety for a reductive group G from the module of integral ordinary distributions. For G=U(n)xU(n+1), we construct the Bessel periods as H-invariant distributions, in both definite and indefinite cases, where H is the diagonal subgroup of G appearing in the Gan-Gross-Prasad conjecture. Finally we relate such period to the characteristic divisor of the Selmer group of the standard Galois representation over the eigenvariety.