Gelfand pairs and gamma factors mod ℓ
报告专家：Robin Zhang博士（美国麻省理工大学）
报告时间：2024年1月19日下午14:30-15:30
报告地点：西南中心516
报告摘要：I will discuss two uniqueness phenomena in representation theory with applications to number theory. First, we have the classical complex theory of Gelfand pairs and its generalizations; this has many applications to automorphic forms, such as the uniqueness of Whittaker models and the non-vanishing of the central value of triple product L-functions. Second, we have the local converse theorems that say that irreducible representations have unique Rankin–Selberg gamma factors; with this, one can characterize the local Langlands correspondence for GL(n) by compatibility of gamma factors. We will show how both phenomena can be extended to positive characteristic using two techniques involving module projectivity. The second part of this talk is based on joint work with J. Bakeberg, M. Gerbelli-Gauthier, H. Goodson, A. Iyengar, and G. Moss.
专家简介：Robin Zhang现任美国麻省理工大学NSF Postdoctoral Fellow，他2023年5月于美国哥伦比亚大学取得博士学位，导师为著名数学家Michael Harris教授。Robin Zhang主要从事数论、自守表示以及丢翻图几何等方向的研究，部分研究成果目前已发表于Int. Math. Res. Not. ，Math. Res. Lett.，Annales de l'Institut Fourier等多个国际期刊。
邀请人：许宾
