报告摘要：
We 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. Thus, KPZ phenomenon exhibits both universality and integrability.
In the second part of the talk I plan to introduce an alternative geometrical approach to the problem of the KPZ universality. It provides an even broader point of view on the problem of universal statistical behavior.
报告人简介：
卡宁曾于2000年受邀在巴塞罗那举行的欧洲数学大会（European Congress of Mathematics）上作报告；2013年成为西蒙斯基金会（Simons Foundation）会士；2017年担任法国国际数学研究中心（CIRM）的让-莫莱（Jean-Morlet）讲席教授；2018年受邀在里约热内卢举办的国际数学家大会（ICM）上作报告。2021年，他荣获洪堡奖（Humboldt Prize，又称洪堡研究奖），以表彰其毕生在数学研究领域取得的杰出成就。
