Geometry Seminar

Date: April 11, 2022

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Markus Hunziker, Baylor University

Title: Classical invariant theory, Hermitian symmetric spaces, and covariant differential operators

Abstract: Classical invariant theory is concerned with the explicit calculation of syzygies of rings of invariants and modules of covariants for the classical groups. In this talk, I will explain how some of these computations can be organized by using a diagrammatic description of certain highest weight categories related to Hermitian symmetric spaces. I will then show how this approach leads to the solution of several previously open problems in invariant theory. If time permits, I will also explain how the boundary maps of the minimal free resolutions of modules of covariants correspond to so-called covariant differential operators (which are matrix-valued differential operators between holomorphically induced representations.)