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

• Public Lecture: Tuesday 23 Aug., 18:00; Physiology Building 63, Room 348, University of Queensland, St Lucia.

Title: Number theory and the circle packings of Appolonius

• Colloquium: Wednesday 24 Aug., 15:00; Parnell Building 7, Room 222, University of Queensland, St Lucia.

Title: Möbius randomness and dynamics

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

• Number theory and the circle packings of Appolonius

Like many problems in number theory, the questions that arise from packing the plane with mutually tangent circles are easy to formulate but difficult to answer. We will explain the fundamental features of such packings and how modern tools from number theory, algebra and combinatorics are being used to answer some of these old questions.

• Möbius randomness and dynamics

The Möbius function \mu(n) is minus one to the number of distinct prime factors of n if n has no square factors and zero otherwise. Understanding the randomness (often referred to as the "Möbius randomness principle") in this function is a fundamental and very difficult problem. We will explain a precise dynamical formulation of this randomness principle and report on recent advances in establishing it and its applications.