06/07/2018, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Miguel Tierz, Faculdade de Ciências ULisboa
Minors of Toeplitz matrices, symmetric functions and random matrix ensembles
We study minors of Toeplitz matrices, using the theory of symmetric functions. The symbols of the Toeplitz matrices can either be in the Szegö class or have Fisher-Hartwig singularities and the results apply both to minors of finite and of large dimension. As an application, also using results on inverses of Toeplitz matrices, we obtain explicit formulas for a Selberg-Morris integral and for specializations of certain skew Schur polynomials. We also discuss the intimate relationship with random matrix theory and the ensuing applications.
