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