Extrema of the Characteristic Polynomial of CβE Matrices

Explore the mathematical properties of logarithmically correlated fields through this 58-minute conference talk examining the extrema of characteristic polynomials of CβE matrices. Delve into groundbreaking research that proves the maximum of the logarithm of the characteristic polynomial, when properly centered, converges to the sum of a Gumbel random variable and an independent random variable Z, validating the renowned Fyodorov–Hiary–Keating conjecture. Learn about joint work with Elliot Paquette that advances understanding of these complex mathematical structures, and discover recent developments in identifying the specific properties of the random variable Z in this cutting-edge area of mathematical research.