Random Matrix and SYK model
The random matrix theory was started in the 1930s, with notable contributions made by J. Wishart, Baolu Xu and others. During the 1950s of last century, physicist E. Wigner introduced random matrices as a means to simulate the nuclei of heavy atoms, predicting that the spacing between the spectra of heavy atomic nuclei should mirror the spacing between the eigenvalues of random matrices. Many prominent mathematicians also worked on this theory and made very important progress. In this talk, I will begin with some basics on the random matrix theory, then I will discuss some results obtained by my collaborators and myself. Next I will briefly discuss the SYK model, which is now a very active research area in physics. Our objective is to establish a mathematical theory for the SYK model, and I will present some advancements we made as well as some open problems.
Overview
Presenters
Prof. Gang Tian
Brief Biography
Tian Gang is a member of the Chinese Academy of Sciences, member of the American Academy of Arts and Sciences, Chair Professor at Peking University, Director of the Beijing International Center for Mathematical Research, President of Great Bay University (in preparation), Former President of the Chinese Mathematical Society（2020-2023).
Tian Gang solved a series of fundamentally important problems in geometry and mathematical physics. Most notably, he did pioneer work in the study of Kähler-Einstein metrics, introduced the notion of K-stability, and proved the existence of Kähler-Einstein metric on K-stable Fano manifolds. With collaborators, he established the mathematical foundation of quantum cohomology, constructed the Gromov-Witten invariants of symplectic manifolds, and solved the non-degenerate case of the Arnold conjecture in symplectic geometry. He made outstanding contributions to the mathematical theory of higher dimensional gauge fields and discovered the deep connection between self-dual Yang-Mills connections and calibrated geometry. He also initiated the analytic minimal model program which uses methods from geometric analysis to study birational geometry and together with others, made substantial progress. More recently, he made very important contributions to the geometric analysis of low dimensional manifolds and various types of curvature flows.
He received the 19th Alan Waterman Award from the National Science Foundation of the United States and the Oswald Veblen Prize from the American Mathematical Society. He was an invited speaker at the International Congress of Mathematicians in 1990, and plenary speaker at the International Congress of Mathematicians in 2002.