Tobias Ekholm: Knot contact homology, Chern-Simons, and topological stringsĭmitry Khavinson: 'Between two truths of the real domain, the easiest and shortest path quite often passes through the complex domain.' P. Volodymyr Mazorchuk: (Higher) representation theory Yulij Ilyashenko: Towards the global bifurcation theory on the plane Mattias Jonsson: Complex, tropical and non-Archimedean geometry Jeff Steif: Noise Sensitivity of Boolean Functions and Critical Percolation Viviane Baladi: Analytical tools for dynamics with singularities, including Sinai billiardsĪrno Kuijlaars: Universality in random matrix theory James Norris: Scaling limits for planar aggregation with subcritical fluctuations Leslie Greengard: Inverse problems in acoustic scattering and cryo-electron microscopy Philip Maini: Modelling collective cell motion

DownloadsĪrno Kuijlaars: Universality in random matrix theory (audio and video, mp4) I will also discuss the more recently discovered universal behavior for eigenvalues and singular values of products of random matrices. In the talk I will give an overview of these developments. For example the breaking of a spectral gap corresponds to a special solution of the Painlevé II equation. This universality phenomenon was observed by Wigner in the 1950s and proved by mathematicians in great generality since the 1990s.ĭeviations from universality correspond to phase transitions in limiting eigenvalue behavior that can be analyzed with nonlinear special functions: the Painlevé transcendents. The local repulsion of eigenvalues leads to microscopic limit laws that are independent of the fine details of the random matrix model.

Föreläsare: Professor Arno Kuijlaars, Katholieke Universiteit Leuvenġ5:15-16:15 Colloquium lecture by Arno Kuijlaars (Room Oskar Klein, AlbaNova)ġ6:15-17:00 SMC social get together with refreshments AbstractĮigenvalues of large random matrices have a remarkable behavior as the size of the matrices tends to infinity.

Random matrix number theory