Extremes for the Two Dimensional Liouville Model

This lecture explores the establishment of a strong coupling between the Liouville model and the Gaussian free field on the two-dimensional torus, demonstrating how the difference between these two fields can be bounded uniformly by a random constant. Learn about the application of this coupling to prove that the maximum of the Liouville field converges in distribution to a randomly shifted Gumbel distribution. The 54-minute presentation, delivered at the Hausdorff Center for Mathematics, represents joint work with Michael Hofstteter and provides valuable insights into extreme value theory for two-dimensional random field models.