This year's Mahler Lecturer is Peter Sarnak, of Princeton University. He will be visiting various Australian universities throughout August 2011.

• Tues 15 Aug. at 18:00; Laby Theatre, David Caro Building, University of Melbourne.

Title: Randomness in Number Theory

Professor Sarnak is a major figure in modern analytic number theory, with research interests also in analysis and mathematical physics. He has received many awards for his research including the Polya prize in 1998, the Ostrowski prize in 2001, the Conant prize in 2003 and the Cole prize in 2005.

Biography

Professor Peter Sarnak grew up in South Africa and moved to the US to study at Stanford University, where he obtained his PhD in mathematics in 1980. After appointments at the Courant Institute, New York, and Stanford, he moved to Princeton in 1991 where he has been ever since. Currently he is both the Eugene Higgins Professor of Mathematics at Princeton University and Professor at the the Institute for Advanced Study in Princeton. In 2002, he was made a member of the National Academy of Sciences in the USA and a Fellow of the Royal Society.

Abstract

By way of concrete examples we discuss the dichotomy that in number theory the basic phenomena are either very structured or if not then they are random. The models for randomness for different problems can be quite unexpected and understanding, and establishing the randomness is often the key issue. Conversely the fact that certain number-theoretic quantities behave randomly is a powerful source for the construction of much sought-after pseudo-random objects.