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.

Introduction
Overview
simplicial homology
boundary operator
cohomology space
commology group
differential
Ramcomology
Local systems
Linear D
Riemann Hilbert Correspondence
Summary
Topology
Rigidity
Finitely presented groups
Isomorphic representations
Rigid local systems
Magulis super agility
Lebowsky and Magulis
Attribute geometry
Basic properties
Complex variations
Simpsons motivity
Geometric origin
Monotony theorem
Simpson contracture
Integrality
The plan
Theorem
French mathematicians
Continuous local systems
Glocal systems
Applications