Geometric deformation of Selberg integral and aspects of quantum geometry (Pavel Wiegmann, Chicago)

14.07.2026 15:30 – 16:30

In his 1944 paper Remarks on a Multiple Integral, Atle Selberg evaluated what later became known as the Selberg integral:


What happens if one deforms the support of the integral by replacing the interval [0,1] with an arbitrary Jordan arc γ? We show that, in the limit of a large number of variables N, the integral converges to the spectral determinant of the Laplace operator on the slit domain C\γ.
More generally, the Selberg integral exhibits an emergent conformal covariance under deformations of its support. This provides a probabilistic (or quantum) counterpart of Fekete's theory, of finite finite-dimensional approximations of conformal maps.
Related works: A. Etterer, A. Zabrodin, K. Johansson, F. Viklund, K. Courteaut

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre