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

• Public Lecture, Thursday 11 Aug., 18:00 WST; Weatherburn Lecture Theatre, University of WA.

Title: Randomness in number theory

• Colloquium lecture via Access Grid, Friday 12 Aug., 13:30 WST; University of WA.

Title: Thin integer matrix groups and the affine sieve

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.

Abstracts

• Randomness in number theory

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 forrandomness 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.

• Thin integer matrix groups and the affine sieve

Infinite index subgroups of integer matrix groups like \operatorname{SL}(n,Z) which are Zariski dense in \operatorname{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.

Access Grid

If you want to listen to the AGR lecture on August 12 in ELT1 from 1.30–2.30pm WST, please book an AGR room from 1–3pm WST or 3–5pm EST, and let Jason Tan (jason.tan@uwa.edu.au) and Jason Bell (jason.bell@arcs.org.au) know that you will be participating.

Links

• UWA, Year of Maths