主持人：刘博 教授
报告内容介绍：
Holomorphic cusp forms on the modular surface are classical objects of modern number theory. Their arithmetic content is carried by the special Hecke eigenforms, whose L-functions encode deep arithmetic; the modular discriminant, with its Ramanujan tau function, is a familiar example. For a form of large weight, it is natural to ask how its mass distributes over the surface, whether it spreads evenly or concentrates in small regions, and how large it can get. For the Hecke eigenforms these questions have been studied extensively with arithmetic methods, which reveal attractive properties such as equidistribution and slow growth in the supremum norm. Yet Hecke eigenforms are rare within the much larger, largely unexplored family of holomorphic cusp forms. In this talk I take an analyst's view, addressing the same questions for general and generic forms with tools from analysis, geometry, and probability, and comparing them with their Hecke counterparts. Joint work with Bingrong Huang, Peter Humphries, and Melissa Tacy.
主讲人介绍：
Xiaolong Han obtained his PhD in mathematics from Wayne State University in 2012. He then spent four years as a postdoctoral fellow at the Australian National University, and since 2016 has been a faculty member at California State University, Northridge. His research lies in global harmonic analysis and quantum chaos, where he studies the size and distribution of eigenfunctions and automorphic forms in relation to the underlying global geometry and chaotic dynamics.
