Prime Numbers, Quantum Chaos, and Pseudo-Laplacians
Speaker: Amy DeCelles, University of St. Thomas
Date & Time:
12:00 PM - 1:00 PM
Owens Science Center (OWS 250)
Abstract: Prime numbers are the most elementary numbers after the whole numbers, yet primes are subtle. Mathematicians have been seeking to understand the patterns in primes for centuries. The celebrated Riemann Hypothesis is the archetype of an unanswered question involving primes. Riemann's brilliant observation was the precise connection between primes and zeroes of a complex-valued function now known as the Riemann zeta function. Hilbert proposed a strategy for proving the Riemann Hypothesis: finding a positive symmetric operator whose eigenvalues are parametrized by zeros of zeta. Striking correlations have been observed between the eigenvalues of random matrices and the zeros of zeta, raising hopes that there might be a connection with quantum chaoes, but there is no known casual relationship between these phenomena. Recent work of Garrett and Bombieri, picking up on work of Colin deVerdiere, whose eigenvalues correspond to zeroes of the zeta function.
Biographical Information: Amy DeCelles is an Assistant Professor in the Mathematics Department at the University of St. Thomas.