SEMINAR: Colloquium: Thin integer matrix groups and the affine sieve

Colloquium by the 2011 Mahler Lecturer

Peter Sarnak (Princeton University)

will speak on

Thin integer matrix groups and the affine sieve

at 1:30pm on Friday 12th of August in Engineering Lecture Theatre 1

Abstract: Infinite index subgroups of integer matrix groups like SL(n,Z) which are Zariski dense in SL(n) arise in geometric diophantine problems (eg Integral Apollonian Packings) as well as monodromy groups associated with families of varieties. One of the key features needed when applying such groups to number theoretic problems is that the congruence graphs associated with these groups are "expanders".We will introduce and explain these ideas and review some recent developments especially those connected with the affine sieve.

About the speaker: 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.

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