Probability Seminar - Anderson Localization-Delocalization Conjecture from the Perspective of Random Matrix Theory
报告人：杨帆（清华大学)
时间：2025-10-27 14:00-16:30
地点：四元厅
Abstract：The phenomenon of metal-insulator transition in disordered quantum systems has been a central topic of study in probability theory and mathematical physics since Anderson's seminal work on random Schrödinger operators, also referred to as the Anderson model. While there has been significant progress in understanding the localization of Anderson model, the understanding of Anderson delocalization is far less developed—almost nonexistent in the literature. In this talk, I will begin with the conjecture about the Anderson localization-delocalization transition. Next, I will briefly review some recent advancements regarding this conjecture from the perspective of random matrix theory, focusing on the celebrated random band matrix model. I will survey some recent mathematical results concerning the spectral properties of random band matrices and highlight some important ideas that have emerged during this process. Finally, I will summarize several open problems that remain to be addressed in this area.
Bio: 杨帆现为清华大学丘成桐数学科学中心的副教授。于2009年本科毕业于清华大学，2014年获得香港中文大学物理学博士学位，2019年获得加利福尼亚大学洛杉矶分校的数学博士学位，2019年至2022年期间为宾夕法尼亚大学统计与数据科学系的博士后研究员。他的研究领域为概率和统计，主要关注随机矩阵理论及其在概率论、数学物理、高维统计等领域内的应用。
