报告时间：2025年5月26日（星期一）9:00-10:30
报告地点：翡翠湖校区翠六教312室
报 告 人：Jerome William Hoffman 教授
工作单位：路易斯安那州立大学
举办单位：数学学院
报告简介：
This is a report of work with Winnie Li, Ling Long and Fang-Ting Tu. The theme is to relate hypergeometric character sums to traces of Hecke operators on modular forms in interesting cases. These arise from certain arithmetic triangle groups. Especially we consider the quaternion algebra B over Q with discriminant D = 6. In that case, quotients of the upper half plane by the units in these algebras give rise to Shimura curves, which are moduli spaces for 2-dimensional abelian varieties with quaternion multiplication (QM).
In the talk, I will explain the geometric background of this problem, in particular the Eichler-Shimura theory relating modular forms to parabolic cohomology, both in the complex-analytic and in the l-adic étale setting. The key result, due to Kuga-Shimura, computing the zeta functions of the fiber spaces of abelian varieties in terms of Hecke polynomials, allows one to relate these hypergeometric character sums to traces of Hecke operators on spaces of modular forms.
报告人简介：
Jerome William Hoffman, 美国路易斯安那州立大学教授。1973年本科毕业于普林斯顿大学，1977年博士毕业于哈佛大学，师从菲尔兹奖得主（1970）Hironaka。长期从事代数几何与数论的研究，主要研究成果发表在Duke Math.J, Mem.Amer.Math.Soc, Advance.Math等多个有影响力的期刊上。