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

Date & Venue: Monday 15 August, 14:00; Science Lecture Theatre, Monash University, Clayton.

Title: Zeroes and nodal lines of modular forms

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

One of the consequences of the recent proof by Holowinski and Soundararajan of the holomorphic "Quantum Unique Ergodicity Conjecture" is that the zeros of a classical holomorphic Hecke cusp forms become equidistributed as the weight of the form goes to infinity. We review this as well as some finer features (first discovered numerically) concerning the locations of the zeros as well as of the nodal lines of the analogous Maass forms.The latter behave like ovals of random real projective plane curves, a topic of independent interest.