Another look at the KPZ problem
演讲者
时间
2024年11月04日 17:00 至 17:45
地点
A6-101
线上
Zoom 388 528 9728
(BIMSA)
摘要
I will start by introducing the phenomenon of the KPZ (Kardar-Parisi-Zhang) universalty. KPZ problem was a very active research area in the last 20 years. The problem is essentially interdisciplinary. It is related to such fields as probability theory, statistical mechanics, mathematical physics, PDE, SPDE, random dynamics, random matrices, and random geometry, to name a few. In the most general form the problem can be formulated in the following way. Consider random geometry on the two-dimensional plane. We shall think about it as a random landscape of hills, mountains, and valleys. The main aim is to understand the asymptotic statistical properties of the length of the geodesic connecting two points in the limit as distance between the endpoints tends to infinity. One also wants to study the geometry of random geodesics, in particular how much they deviate from a straight line. It turns out that the limiting statistics for both the length and the deviation is universal, that is it does not depend on the probability distribution of the random landscape. Moreover, many limiting probability distributions can be found explicitly.
演讲者介绍
Khanin received his PhD from the Landau Institute of Theoretical Physics in Moscow and continued working there as a Research Associate until 1994.[2] Afterwards, he taught at Princeton University, at the Isaac Newton Institute in Cambridge, and at Heriot-Watt University before joining the faculty at the University of Toronto. Khanin was an invited speaker at the European Congress of Mathematics in Barcelona in 2000. He was a 2013 Simons Foundation Fellow. He held the Jean-Morlet Chair at the Centre International de Rencontres Mathématiques in 2017, and he was an Invited Speaker at the International Congress of Mathematicians in 2018 in Rio de Janeiro. In 2021 he was awarded The Humboldt Prize, also known as the Humboldt Research Award, in recognition of his lifetime's research achievements.