Special Colloquium, Professor and Head, Anantharam Raghuram, Indian Institute of Science Education and Research, BRNG B268
Tuesday, Dec 11 3:30 pm - 4:30 pm
Title: Automorphic Number Theory. -- Abstract: I will begin my talk by introducing the two major inputs to my research: (1) L-function: an L-function is a function L(s, M) of a complex variable s that is attached to some interesting arithmetic or geometric object, say, M; a basic principle is that the special values of such an L-function at critical points give structural information about M. (2) Cohomology: given a smooth manifold X and a sheaf F on X, one attempts to understand the cohomology groups H*(X, F); producing nontrivial cohomology classes when X is a locally symmetric space may be construed as constructing interesting automorphic forms on the ambient group that determines X. After explaining such inputs, I will discuss a working principle that underlies much of my recent work: given an analytic theory of L-functions, interpret the underlying integrals in terms of maps in cohomology. Finally, I will give glimpses into my recent results, ongoing work, and the work I propose to do in the near future, that concern the arithmetic properties of the special values of automorphic L-functions using analytic techniques from the Langlands program and geometric techniques from the cohomology of locally symmetric spaces.
Tuesday, Apr 16 3:30 pm - 4:30 pm