The school will focus on important trends in modern mathematical physics and complex analysis related to multivariate probability theory and integrable systems.

We will have a lecture series on random matrix theory, covering asymptotic spectral properties of classical random matrix ensembles, as well as applications and key techniques, including the Stieltjes transform method and the supersymmetry methods. A course on zeros of random functions will cover various properties of zeros of random polynomials and analytic functions. Finally, a course on integrable nonlinear partial differential equations, which includes the nonlinear Schrödinger equation as a prototype, will introduce the widely used inverse scattering transform method with detailed methods for solving the Riemann-Hilbert problem. All lectures will be given by leading experts in their fields:

• Yan Fyodorov (King's College London)

• Leonid Pastur (King's College London/B. Verkin ILTPE of NASU)

• Mariya Shcherbina (Institute of Science and Technology Austria (ISTA) / B. Verkin ILTPE of NASU)

• Dmitry Shepelsky (B. Verkin ILTPE of NASU)

• Mikhail Sodin (Tel Aviv University)

• Bálint Virág (University of Toronto)

Programme will also include problem-solving sessions, a poster session, and discussions in groups. The problem sessions will be led by Ievgenii Afanasiev, Yan Rybalko, Roman Sarapin (all three from B. Verkin ILTPE of NASU), and Oren Yakir (Stanford University, remotely).