Noncommutative geometry and number theory

Paula Beazley Cohen

This talk will give a general overview of recent work exploring relationships between the statistics of prime numbers and non-commutative statistical mechanics. The departure point is work of Bost-Connes who several years ago constructed a C^{∗}-dynamical system with partition function the Riemann zeta function and a phase transition at the pole of the zeta function. More recently, this older work has inspired a suggested approach of Alain Connes to the Riemann Hypothesis.