Linear Systems and Differential Equations in Random Matrix Theory

Explore a 50-minute semi-plenary talk by Gordon Blower from Lancaster University, UK, on linear systems and differential equations in random matrix theory. Delve into the solution of nonlinear differential equations using linear systems, focusing on Hankel integral operators and Fredholm determinants. Examine the connections between Schrödinger differential operators and Hankel integral operators, and discover solutions to the sinh-Gordon PDE and Painlevé III' transcendental ordinary differential equation. Learn about applications in random matrix theory and MIMO wireless communications. Investigate topics such as controllability and observability operators, Howland operators, theta and tau functions, scattering functions, matrix potentials, and the Gelfand-Levitan equation. Gain insights into Hankel determinants, Painlevé equations, random matrix models, and the free logarithmic Sobolev inequality. This collaborative work with Yang Chen and Ian Doust offers a comprehensive exploration of advanced mathematical concepts and their practical applications.