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

• Public Lecture: Wednesday 17 Aug., 17:30; Manning Clarke Centre Theatre 3, Australian National University, Canberra.

Title: Number theory and the circle packings of Appolonius

• Colloquium: Thursday 18 Aug., 15:30; Manning Clarke Centre Theatre 4, Australian National University, Canberra.

Title: Horocycle flows at prime times

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.

• Horocycle flows at prime times

The distribution of individual orbits of unipotent flows in homogeneous spaces are well understood thanks to the work of Marina Ratner. It is conjectured that this property is preserved on restricting the times from the integers to primes, this being important in the study of prime numbers as well as in such dynamics. We review progress in understanding this conjecture, starting with Dirichlet (a finite system), Vinogradov (rotation of a circle or torus), Green and Tao (translation on a nilmanifold) and Ubis and Sarnak (horocycle flows in the semisimple case).