Lecture Series on “Arithmetic in Geometry”  #4
Lecture Series on “Arithmetic in Geometry”  #4

Professor Gopal Prasad , University of Michigan
Fine Hall 322
In the next two talks, I will discuss another wellknown problem which was very nicely formulated by Mark Kac as "Can one hear the shape of a drum?", and its solution, for arithmetic quotients of symmetric spaces, obtained in a joint work (in Publ Math IHES) with Andrei Rapinchuk. For the solution, we introduced a notion of "weak commensurability" of arithmetic, and more general Zariskidense, subgroups and derive very strong consequences of weak commensurability.