description: My talk will describe work which points towards a spectral interpretation of the zeros of L-functions (such as, for example, the Riemann Zeta function).
Hilbert and Polya conjectured that there might be some natural operator whose characteristic equation corresponds to the Riemann Zeta function. This would provide a means to tackle the Riemann Hypothesis since certain operators have eigenvalues with nice properties- either lying on a line (such as Hermitian operators) or on a circle (such as unitary operators).
Recent theoretical and numerical evidence indicate that there does indeed seem to be a spectral interpretation, for the zeros in terms of the classical compact groups.