報告時間：2025年5月26日（星期一）9:00-10:30
報告地點：翡翠湖校區翠六教312室
報 告 人：Jerome William Hoffman 教授
工作單位：路易斯安那州立大學
舉辦單位：數學學院
報告簡介：
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.
報告人簡介：
Jerome William Hoffman, 美國路易斯安那州立大學教授。1973年本科畢業于普林斯頓大學，1977年博士畢業于哈佛大學，師從菲爾茲獎得主（1970）Hironaka。長期從事代數幾何與數論的研究，主要研究成果發表在Duke Math.J, Mem.Amer.Math.Soc, Advance.Math等多個有影響力的期刊上。
