Hans Zassenhaus Distinguished Lectures



by Peter Sarnak

Eugene Higgins Professor of Mathematics, Princeton University

Professor of Mathematics, Courant Institute, New York University


Wednesday, November 3

Thursday, November 4

Friday, November 5


4:30 - 5:30 PM


MBI lecture hall (MA240)

Mathematics Department

Ohio State University


"Arithmetic and analysis on locally symmetric spaces"


Abstract:   Analysis and arithmetic on locally symmetric spaces is at the heart of many developments and applications of the modern theory of automorphic forms. The applications include ones to classical problems in number theory and more recently to ones in mathematical physics (especially "quantum chaos"). After a general introduction we will discuss  modular surfaces in some detail. In the second and third lectures will  discuss  the general case, concentrating on the basic questions of the location of  the spectrum of the natural invariant operators that act on these spaces  (that is, the general "Ramanujan Conjectures") and the issue of the size of their eigenfunctions and of the corresponding L-functions. We will also describe some recent ergodic theoretic tools that have proven  to be  powerful  in connection with problems of equi-distribution on these spaces.




For further information or to inquire about remote videoconferencing, contact: Herb Clemens clemens@math.ohio-state.edu