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