科研进展与学术交流报告会  

（第44期）

报告人一： 曾强 副研究员（应用数学研究所）    

题目一：Replica symmetry breaking and landscape complexity for spin glasses  

摘 要：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, the physicist Giorgio 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 by breaking the symmetry of replicas infinitely many times at low temperature. 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 work and show that his prediction on infinite replica symmetry breaking holds at zero temperature for the more general mixed p-spin model. An 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. Connection to PDE, random matrices and combinatorial optimization will be mentioned. This talk is based on joint works with Antonio Auffinger (Northwestern University), Wei-Kuo Chen (University of Minnesota), Hao Xu (University of Macau) and Haorao Yang (Peking University).  

报告人二： 许媛媛 助理研究员（应用数学研究所）    

题目二：Recent progress on extreme eigenvalue problem in random matrix theory  

摘要：We report some recent progress on the extreme eigenvalue problem of large random matrices.  In the first part of the talk, we consider a classical Hermitian random matrix (Wigner matrix) and show the Tracy-Widom law for the largest eigenvalue with the optimal speed of convergence.  In the second part of the talk, we study a non-hermitian matrix with i.i.d. entries and prove the Gumbel law for the spectral radius. These results are based on several joint work with Kevin Schnelli, Giorgio Cipolloni, L szl  Erd？s, and Dominik Schr？der.    

时  间：2023.10.20(星期五), 10:40-12:00    

地  点：南楼204会议室/腾讯会议374-6743-0937    

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