Gergely Bérczi (Aarhus University) - Enumerative applications of non-reductive GIT
Channel: Jesús Martínez-García
Date: 2020-12-10

Gergely Bérczi (Aarhus University) - Enumerative applications of non-reductive GIT.

Talk delivered at EDGE 2020 (online) Workshop "Explicit K-stability and Moduli Problems".

https://www.maths.ed.ac.uk/cheltsov/edge2020/

Abstract: Polynomial reparametrisation groups form the symmetries of jets of holomorphic curves in complex manifolds. They play central role in various classical problems in geometry. I report on recent work in two, seemingly unrelated questions: (i) degeneracy loci of holomorphic maps between complex manifolds and Thom polynomials of singularities and (ii) the Green-Griffiths-Land and Kobayashi hyperbolicity conjectures. I will explain why moduli of jets is a link between the two, and how recently developed intersection theory of non-reductive GIT quotients led to the proof of the polynomial Kobayashi conjecture, and resulted in new formulas for Thom polynomials.