Invariant theory and the Gaiotto-Rapcak conjectures by Prof. Andrew Linshaw, University of Denver

Invariant theory and the Gaiotto-Rapcak conjectures by Prof. Andrew Linshaw, University of Denver, Friday April 25, 1:00 – 1:50pm, North Science Building 015, Wachenheim, Faculty Seminar

Abstract: I will outline the basics of representation theory and classical invariant theory, and then introduce vertex algebras, which first appeared in physics in the 1980s and were axiomatized by Richard Borcherds in his proof of the Moonshine conjecture. I will then explain some dualities among vertex algebras which were conjectured in 2017 by the physicists Davide Gaiotto and Miroslav Rapcak, and proven in my recent work with Thomas Creutzig. The proof is essentially an application of Hermann Weyl’s fundamental theorems of invariant theory which appeared in his 1939 monograph “The Classical Groups: Their Invariants and Representations”.