The rigidity of noncommutative motives (after Efimov) by Maxime Ramzi

Abstract:
 The goal of this lecture series is to present some of the developments around the theory of noncommutative motives arising from Efimov’s work. I will focus on one of his main theorems, namely the rigidity of the category of motives. I will introduce rigid and dualizable categories to motivate and prepare the grounds for this theorem; give a proof of it; and, to an extent depending on time, present applications of this theorem and surrounding methods. 

Lecture 2 (Video)

Lecture 3 (Video)

Geometric Extensions by Chris Hone

Abstract

Geometric representation theory gives that the geometry of types of algebraic varieties encodes the representation theory of associated objects. I’ll attempt to tell part of this story, through various examples.

The main geometric/categorical tool used in this story is the six functor formalism, which encodes (but is much richer than) ordinary (co)homology. I’ll then aim to explain some recent work, constructing interesting “sheaves” on singular varieties using the (formal) six functor formalism. This work is joint with Geordie Williamson.

Lecture 1 (Video)

Lecture 2 (Video)

Lecture 3 (Video)