Wednesday 6 March 2019, 16:00-17:00 in HG03.085
Walter van Suijlekom (RU)
Entropy and the spectral action in noncommutative geometry
After a gentle introduction to noncommutative geometry, and spectral triples in particular, we formulate a corresponding fermionic second-quantized theory. This involves a \(C^*\)-dynamical system to which we relate a (unique) KMS-state. We show that the (von Neumann) entropy of this state is given by the spectral action of the spectral triple for a specific universal function. We then analyze the structure of this function and show that it can be written as a Laplace transform. Finally, we find a surprising relation between this function and the Riemann zeta function. (based on joint work with Ali Chamseddine and Alain Connes).