### Thursday, July 16

## SS4

The George Polya Prize

4:45 PM-5:45 PM

*Chair: John Guckenheimer, President, SIAM; and Cornell University*

*Room: Convocation Hall*

The Polya Prize, established in 1969, is awarded in 1998 for notable contributions in an area of inerest to George Polya. The prize is broadly intended to recognize specific recent work. The 1998 recipients are Percy Deift, Xin Zhou, and Peter Sarnak. Of the three winners, Xin Zhou and Peter Sarnak will each give a presentation.

**Steepest Descent Method for Riemann-Hilbert Problems in Pure and Applied Mathematics**
A surprisingly large variety of problems in mathematics can be formulated in terms of a Riemann-Hilbert Problem (RHP). Typically, such RHP's contain oscillatory multipliers $e^{ix\theta(z)}$, and the basic analytic issue is to compute explicitly, with classical error bounds, the asymptotics of the solution of the RHP as the (external) parameter $x$ becomes large. We describe a steepest-descent type method introduced by Deift and Zhou to analyze such RHP's as $x\to\infty$. This leads in turn to the solution of a large variaty of asymptotic problems in pure
and applied mathematics.

**Zeros of Zeta Functions and Symmetry**
The high zeros of a function like the Riemann zeta functions or the low zeros of families of such functions apparently obey distribution laws associated with eigenvalues of matrices in large classical
groups. The speaker will give a brief review of what is known about this phenomenon and its cause.

**4:45 Introduction and Presentation of Award **
- John Guckenheimer, President, SIAM; and Cornell University
**4:55 Steepest Descent Method for Riemann-Hilbert Problems in Pure and Applied Mathematics**
- Xin Zhou, Duke University
**5:20 Zeros of Zeta Functions and Symmetry**
- Peter Sarnak, Princeton University

LMH Created: 3/16/98; MMD Updated: 6/15/98