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Visit by 2011 Mahler Lecturer, Professor Peter Sarnak

2011 Mahler Lecturer

Peter Sarnak
Eugene Higgins Professor of Mathematics, Princeton University
and Professor, Institute of Advanced Studies


2pm, Monday 15th August
Lecture Theatre S14, Building 29
Monash University Clayton

Zeros and nodal lines of modular forms

One of the consequences of the recent proof by Holowinski and Soundararajan of the holomorphic "Quantum Unique Ergodicity Conjecture" is that the zeros of the classical holomorphic Hecke cuspforms 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.

Lecture Poster

The Mahler lectures are a biennial activity organised by the Australian Mathematical Society with the assistance of the Australian Mathematical Sciences Institute.

Contact: Daniel Delbourgo, School of Mathematical Sciences, Monash University (daniel.delbourgo@monash.edu)

During his Melbourne visit, Professor Peter Sarnak will also deliver two public lectures:

Monday Aug 15, University of Melbourne, 6pm, Laby Theatre, David Caro Building, “Randomness in number theory”.
Tuesday Aug 16, La Trobe University, 1pm, Szental Lecture Theatre, “Chaos, quantum mechanics and number theory”.

Professor Peter Sarnak (Photo: Cliff Moore)
Professor Peter Sarnak, Australian Mathematical Society 2011 Mahler Lecturer. (Courtesy of IAS; Photo: Cliff Moore)

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.

Peter 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. He has had 43 PhD students to date, including several who have become major figures in number theory themselves.