报告题目：On mod (p) Hecke algebras of abstract (p)-adic automorphic forms

报 告 人：Truong Xuan Nha 博士后 （北京大学国际数学中心）

报告时间：2026年11月15日（星期日）14:00-15:00

报告地点：数学科学学院114（小报告厅）    

校内联系人：赵路明 副教授    联系方式：84708351-8604

报告摘要： Hecke algebras encode the action of Hecke operators on spaces of automorphic forms. Understanding their structure in characteristic (p) is a central question in the arithmetic of modular forms. In this talk, I will discuss an approach to this question using abstract (p)-adic automorphic forms and smooth representations of (\mathrm{GL}_2(\mathbb{Q}_p)). We obtain a square-root bound for the nilpotence exponent of the local Hecke action. As an application, under a finite-length hypothesis on the relevant representation, we prove that the completed local Hecke algebra is Noetherian of Krull dimension at least two. If, in addition, its cotangent space has dimension at most two, then the algebra is a formal power series ring in two variables. I will explain the main ideas and discuss applications to modular forms modulo (p) and automorphic forms on definite quaternion algebras.

报告人简介：Truong Xuan Nha 是北京大学北京国际数学研究中心的博士后研究员。他于2021年在康涅狄格大学获得数学博士学位，导师为肖梁，并于2021年至2024年在夏威夷大学马诺阿分校担任博士后。他的研究聚焦于 p 进自守形式、特征簇的几何以及非阿基米德动力系统。他的研究成果已被《Annals of Mathematics》和《Peking Mathematical Journal》接收待发表。