**“**LECTURES ON LOCAL SYSTEMS IN ALGEBRAIC-ARITHMETIC GEOMETRY”

**Abstract: **The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is complex local systems. One fundamental problem is to recognize those coming from geometry, and more generally subloci of the moduli space of local systems with special arithmetic properties. This is the object of deep conjectures. We’ll study some consequences of those, notably integrality and crystallinity properties.

**Tuesdays at 2:40 pm**

**Room 520, Mathematics Hall**

**2990 Broadway (117th Street)**

**First lecture: September 13, 2022**