In statistical physics, the study of spin glasses was initialized to describe the low temperature state of a class of magnetic alloys in the 1960s. The Sherrington-Kirkpatrick (SK) model is a mean field approximation of the physical short range spin glass model introduced in the 1970s. Starting in 1979, Parisi wrote a series of ground breaking papers introducing the idea of replica symmetry breaking (RSB), which allowed him to predict a solution for the SK model. Since then, his method has been applied to study various complex systems, which eventually earned him the 2021 Nobel Prize in Physics.

  In this talk, I will first introduce Parisi's conjectures and rigorous results by Talagrand and Panchenko. Then I will show that his prediction on infinite replica symmetry breaking holds at zero temperature for the more general mixed p-spin model. As an example for the application of Parisi's method, I will present Fyodorov and Le Doussal's prediciton on the Hessian spectrum at the global minimum of locally isotropic Gaussian random fields. A partial solution will be provided via landscape complexity.

  报告人简介：曾强本科毕业于北京师范大学，研究生就读于北京大学，博士毕业于伊利诺伊大学香槟分校，后在哈佛大学、伯克利数学科学研究所和西北大学从事博士后研究，现为中国科学院数学和系统科学研究院副研究员。研究领域为非交换概率和自旋玻璃，在非交换鞅和集中不等式，自旋玻璃的副本对称破缺和景观复杂性方面做了一系列工作。相关结果发表于CPAM，CMP，AoP，PTRF等国际高水平期刊。