Understanding the KPZ Problem - A New Perspective on Random Geometry and Universal Statistics

Explore the fascinating world of KPZ (Kardar-Parisi-Zhang) universality in this 45-minute lecture delivered by renowned mathematician Konstantin Khanin at BIMSA. Delve into an interdisciplinary journey spanning probability theory, statistical mechanics, mathematical physics, PDE, SPDE, random dynamics, random matrices, and random geometry. Learn about the fundamental concepts of random geometry on two-dimensional planes, visualized as landscapes of hills, mountains, and valleys, and understand the asymptotic statistical properties of geodesic lengths connecting points at increasing distances. Discover how the limiting statistics for both length and deviation exhibit universal properties, independent of the random landscape's probability distribution, with many limiting probability distributions that can be explicitly determined. Benefit from the expertise of Khanin, a distinguished mathematician whose career includes positions at Princeton University, Isaac Newton Institute, and the University of Toronto, and whose contributions have been recognized with prestigious awards including the 2021 Humboldt Research Award.