An introduction to rigid local systems

Abstract 

A representation of a group G is said to be rigid, if it cannot be continuously deformed to a non-isomorphic representation. If G happens to be the fundamental group of a complex projective manifold, rigid representations are conjectured (by Simpson) to be of geometric origin. In this talk I will outline the basic properties of rigid local systems and discuss several consequences of Simpson‘s conjecture. I will then outline recent progress on these questions (joint work with Hélène Esnault) and briefly mention applications such as the recent resolution of the André-Oort conjecture by Pila-Shankar-Tsimerman.

About the Speaker 

Michael Groechenig is an assistant professor at the University of Toronto. Michael‘s main interests lie at the crossroads of algebraic geometry, number theory, mathematical physics and bouldering. After obtaining his PhD from the University of Oxford in 2013, he was a Chapman fellow at Imperial College London and subsequently a Marie Sklodowska-Curie fellow at Freie Universität Berlin. In 2018, Michael joined the University of Toronto and was awarded an Alfred P. Sloan fellowship in 2022.