Title: Another Look at the KPZ Problem
Speaker: Konstantin Khanin
Institution: Beijing Institute of Mathematical Sciences and Applications
Date & Time: November 29, 2024, 16:00–17:00 (Afternoon)
Location: Room 209, Zhengxin Building, Jilin University
I will begin by introducing the phenomenon of KPZ (Kardar-Parisi-Zhang) universality, a highly active research area over the past 20 years. The KPZ problem is inherently interdisciplinary, touching on fields such as probability theory, statistical mechanics, mathematical physics, partial differential equations (PDE), stochastic partial differential equations (SPDE), random dynamics, random matrices, and random geometry, among others. In its most general form, the problem can be framed as follows: Consider random geometry on the two-dimensional plane, visualized as a random landscape of hills, mountains, and valleys. The core objective is to understand the asymptotic statistical properties of the length of the geodesic connecting two points as the distance between them tends to infinity. Additionally, we aim to study the geometry of random geodesics, particularly how much they deviate from a straight line. Remarkably, the limiting statistics for both the length and deviation are universal, meaning they do not depend on the probability distribution of the random landscape. Moreover, many limiting probability distributions can be explicitly derived.
In the second part of the talk, I will introduce an alternative geometrical approach to the KPZ universality problem, offering a broader perspective on the study of universal statistical behavior. No prior knowledge of the subject will be assumed.
Konstantin Khanin is a professor at the Beijing Institute of Mathematical Sciences and Applications. He previously served as the Chair (academic) of the Department of Mathematical and Computational Sciences at the University of Toronto Mississauga. He earned his PhD from the Landau Institute of Theoretical Physics in Moscow and worked there as a Research Associate until 1994. Subsequently, he taught at Princeton University, the Isaac Newton Institute in Cambridge, and Heriot-Watt University before joining the faculty at the University of Toronto.
Khanin has been an invited speaker at numerous prestigious conferences, including the European Congress of Mathematics (Barcelona, 2000) and the International Congress of Mathematicians (Rio de Janeiro, 2018). He was a Simons Foundation Fellow (2013), held the Jean-Morlet Chair at the Centre International de Rencontres Mathématiques (2017), and received the Humboldt Research Award (2021) in recognition of his lifelong research achievements. His contributions span diverse areas of mathematics, with a focus on stochastic processes, statistical mechanics, and their interdisciplinary connections.
