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.

• Colloquium: Wednesday 25 Sept, 11:00 (WA time, 13:00 EST);
  AGR room, Science Library, University of Western Australia.
  The Cohen-Lenstra heuristics: from arithmetic to topology and back again

Abstract: I will discuss some models of what a “random abelian group” is, and some conjectures (the Cohen–Lenstra heuristics of the title) about how they show up in number theory. I'll then discuss the function field setting and a proof of these heuristics, with Ellenberg and Westerland. The proof is an example of a link between analytic number theory and certain classes of results in algebraic topology (“homological stability”).

• Public Lecture: Wednesday 25 Sept, 18:00 (WA time, 20:00 EST);
  Club Theatre Auditorium, University of Western Australia.
  Two centuries of prime numbers

Abstract: Surprisingly, there have been fundamental new discoveries about prime numbers in the last decade, most recently by Yitang Zhang a few months ago. I’ll survey some of our understanding of prime numbers in a nontechnical fashion, starting with the “music of the primes” — the strange oscillations between regions where primes are more common and more scarce — and concluding with a discussion of Zhang‘s discovery: prime numbers must occasionally come very close to one another.