Abstract: 
Automorphic functions are similar to periodic functions, except they live on a nonabelian group such as the group GL(n) of invertible matrices. They are extremely important in number theory, and sometimes come up also in mathematical physics. In a recent work with David Kazhdan, we have determined the spectrum of the Laplace operators on certain spaces of automorphic functions. While the technical details of this work may be too cumbersome for a colloquium talk, I will try to explain some ideas that go into the proof and also some lessons that may be drawn from it, hopefully also by the physicists. Those interested in a more rigorous mathematical discussion, could perhaps direct their attention to my upcoming talk at https://www.maths.ed.ac.uk/cheltsov/zag/
