Akshay Venkatesh - (Derived) moduli of local systems in number theory [2019]

Abstract
If X is a complex variety, we can form a moduli space M of local systems parameterizing representations of pi_1(X).
One would like to do the same in arithmetic situations -- if X is a curve over a finite field, or the ring of integers of a number field. Here we can only construct a shadow of M, remembering some of its formal geometry. However, there are many indications that a more satisfactory theory should exist, and I will review three of them in my talk.
(Derived) moduli of local systems in number theory
Introductory Workshop: Derived Algebraic Geometry And Birational Geometry And Moduli Spaces January 31, 2019 - February 08, 2019
February 08, 2019 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Akshay Venkatesh (Stanford University)
Location: MSRI: Simons Auditorium
www.msri.org/workshops/862/sch...