University of Chicago and Institute for Information Transmission Problems of the RAS (Kharkevich Institute)
Coulomb gas and Selberg integrals on Riemannian surfaces
Selberg integrals arise as n-dimensional generalizations of the Euler beta integral. Discovered by Selberg in 1941, these integrals raised to prominence since 1980s because of their central role in various, seemingly unrelated disciplines such as the representation theory of infinite dimensional algebras, the theory of orthogonal polynomials, the random matrix theory, combinatorics, and problems of mathematical physics in quantum many-body theory, such as quantum Hall effect. I will review yet another, recently emerged, arena of Selberg integrals - geometry and conformal symmetry.