演讲专家：Wenzhi Luo (The Ohio State University)

演讲主题：Analytic Aspects of Maass Form

演讲时间：2015年7月28日，16:00-17:00

演讲地点：第一教学楼405房间

报告摘要：Maass form, introduced by Hans Maass in his 1949 seminal paper (Math-ematische Annalen 121, 141-183), is a square-integrable eigenfunction of the Laplace-Beltrami operator on a hyperbolic surface S. When S is arithmetic, Maass form, together with the classical modular form as studied by Eisenstein, Jacobi and Poincare are basic examples of automorphic forms. While there are great advances in understanding modular form via powerful algebraic tools such as Galois cohomology and Galois representation, in contrast Maass form is, to a large extent, still quite mysterious and beyond reach. In this general talk, I will survey this fascinating subject and the major approaches such as Selberg trace formula and the spectral theory of automorphic forms, as well as recent progress towards the Ramanujan-Selberg conjecture via Langlands Functo-riality and Analytic Number Theory.