<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META content="text/html; charset=windows-1250" http-equiv=Content-Type>
<META content="MSHTML 5.00.2919.6307" name=GENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV><FONT face=Arial size=2>This year's Paul Turan Memorial Lectures will be
delivered by Peter Sarnak of Princeton University.</FONT></DIV>
<DIV><FONT face=Arial size=2>The lectures are organized by the Janos Bolyai
Mathematical Society and will take place in the Main Lecture Hall of the Renyi
Institute.</FONT></DIV>
<DIV><FONT face=Arial size=2><STRONG>Program of the
lectures:</STRONG></FONT></DIV>
<DIV><FONT face=Arial size=2>Lecture 1 (<STRONG>Tuesday 26 November,
2pm</STRONG>): Sums of squares and Hilbert's 11th problem</FONT></DIV>
<DIV><FONT face=Arial size=2>Lecture 2 (<STRONG>Wednesday 27 November,
2pm</STRONG>): The spectra of modular surfaces</FONT></DIV>
<DIV><FONT face=Arial size=2>Lecture 3 ( <STRONG>Thursday 28 November,
2pm</STRONG>): The spectra of modular surfaces continued.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2><STRONG>Abstract</STRONG>: Hilbert's 11th problem
asks about sums of squares (or more generally representability by integral
quadratic forms) of integers in a number field. Recent progress has led to its
solution. In the first of these lectures we will give an introduction to this
problem and outline the key developments that led to its solution.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>In the second and third lectures we describe the
spectral theory of the Laplacian on modular surfaces indicating how the latter
is used in the solution of the problem of Lecture 1. We also describe other
aspects and applications of this spectral theory, for example to problems of
"Quantum Chaos".</FONT></DIV></BODY></HTML>