C. Random matrices and Mathematical Physics
Principal Investigators: Nam-Gyu Kang (KIAS)
Scientific Partners: Gernot Akemann (Bielefeld), Friedrich Götze (Bielefeld), Ji Oon Lee (KAIST)
Random Matrix theory is an extremely active and exciting research area in Mathematics and Mathematical Physics. It connects for example Analysis, Probability Theory and Combinatorics in various ways. The area is characterized by emerging universal laws for spectral statistics, which apply to surprisingly many phenomena ranging from Number Theory to Quantum Field Theory.
In this project we want to establish new universal limit laws, study rates of convergence as well asymptotic refinements and their applications.
The methods that we plan to apply include concentration of measure techniques, free probability theory and asymptotic analysis of real and complex orthogonal polynomials. This relates to questions in Coulomb gases, Gaussian free fields, conformal field theory and Quantum many-body systems.