Date: May 27, 2007

Prof. Ze'ev Rudnick, Tel Aviv University

Title: Prime numbers and the Riemann zeta function

Abstract: 

Prime numbers are the fundamental constituents of integer arithmetic
and their study constitutes one of the central topics in
mathematics. In recent years this has received extra impetus from
applications in cryptography and e-commerce. In 1859, Riemann
discovered a fundamental relation between the distribution of primes
and the zeros of what is now called Riemann's zeta function, and has
formulated the Riemann Hypothesis concerning the location of these
zeros, which is one of the outstanding problems in mathematics since
then. A bounty of one Million dollars has recently been set for the
solution of this problem. A surprising discovery of recent years is
that the local statistics of the zeros are similar to those of the
energy levels of heavy atoms, and to those of quantum systems whose
classical counterpart is chaotic, and can be modeled by the eigenvalue
statistics of various Random Matrix ensembles. The talk will describe
these phenomena, assuming the audience knows nothing about such
matters.