This year's Mahler Lecturer is Akshay Venkatesh, of Stanford University. He will be visiting various Australian universities throughout September and October 2013. (lecture tour)

Biography

Akshay Venkatesh received his PhD in 2002 from Princeton University and his undergraduate degree from The University of Western Australia. His research is in pure mathematics — specifically, in number theory and related areas. His research interests are in the fields of counting, equidistribution problems in automorphic forms and number theory, in particular representation theory, locally symmetric spaces and ergodic theory. In 2008 he won the SASTRA Ramanujan Prize. This annual prize is for outstanding contributions to areas of mathematics influenced by the genius Srinivasa Ramanujan.

• Public Lecture: Thursday 26 Sept, 18:00 (SA time, 18:30 EST);
  Horace Lamb Lecture Theatre, University of Adelaide.
  How to stack oranges in three dimensions, 24 dimensions, and beyond

Abstract: How can we pack balls as tightly as possible? In other words: to squeeze as many balls as possible into a limited space, what's the best way of arranging the balls? It’s not hard to guess what the answer should be — but it’s very hard to be sure that it really is the answer! I'll tell the interesting story of this problem, going back to the astronomer Kepler, and ending almost four hundred years later with Thomas Hales. I will then talk about stacking 24-dimensional oranges: what this means, how it relates to the Voyager spacecraft, and the many things we don’t know beyond this.

• Colloquium: Friday 27 Sept, 15:00 (SA time, 15:30 EST);
  Horace Lamb Lecture Theatre, University of Adelaide.
  Dynamics and the geometry of numbers

Abstract: It was understood by Minkowski that one could prove interesting results in number theory by considering the geometry of lattices in \mathbb{R}ⁿ. (A lattice is simply a grid of points.) This technique is called the “geometry of numbers.” We now understand much more about analysis and dynamics on the space of all lattices, and this has led to a deeper understanding of classical questions. I will review some of these ideas, with emphasis on the dynamical aspects.