Zhongguancun Number Theory Colloquium

2024 September Colloquium at YMSC

组织者/Organizers：

Koji Shimizu (YMSC), Yihang Zhu (YMSC)

时间/Time：

Fri., 15:00-17:30, Sept. 27, 2024

地点/Venue：

Lecture Hall C654,

Shuangqing Complex Building A

清华大学双清综合楼A座 C654报告厅

报告人/Speakers

Gerard van der Geer

Emeritus Professor of Algebra

Universiteit van Amsterdam

Part-time member of YMSC

Tsinghua University

刘一峰 Yifeng Liu

Permanent Member of IASM

Zhejiang University

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.