An Introduction to Rigid Local Systems

Explore an in-depth introduction to rigid local systems in this lecture by Michael Groechenig from the University of Toronto. Delve into the concept of rigid representations, which cannot be continuously deformed to non-isomorphic representations, and their significance in complex projective manifolds. Examine Simpson's conjecture on the geometric origin of rigid representations and its implications. Investigate the basic properties of rigid local systems and recent progress in the field, including joint work with Hélène Esnault. Discover applications to geometry and number theory, such as the resolution of the André-Oort conjecture. Cover topics including simplicial homology, cohomology spaces, the Riemann-Hilbert Correspondence, finitely presented groups, Magulis super agility, and Simpson's motivity. Gain insights into French mathematicians' contributions and explore the connections between continuous local systems and glocal systems in this comprehensive mathematical exploration.