Operator Limits of Random Matrices (14rit187)


(University of Wisconsin - Madison)

Balint Virag (University of Toronto)


The Banff International Research Station will host the "Operator limits of random matrices" workshop from to .

The emergence of random matrix theory in the 1950s was motivated by nuclear physics, the goal was to model the eigenvalues of large complicated operators. This initiated the study of large random hermitian or symmetric matrices. The study of the asymptotic behavior of the spectrum of such matrices has received another boost in the 1970s when it was discovered (by a chance encounter by Dyson and Montgomery) that the critical zeros of the Riemann zeta-function behave similarly to the point process limit of the eigenvalues of a large Gaussian hermitian matrix.

A conjecture attributed to Hilbert and Polya states that the Riemann hypothesis is true because the imaginary parts of the critical zeros of the zeta-function correspond to the spectrum of a certain unbounded self-adjoint operator. In view of the Dyson-Montgomery connection between the critical zeros of the zeta-function and random matrices it is natural to ask if one can find an unbounded self-adjoint operator whose spectrum is exactly the point process limit of large random matrices. The goal of the research team is to complete a long-standing project related to this and related questions and to provide a better understanding of the limiting objects arising from various random matrix models.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).