Minicourses

There were three minicourses at YMC*A this year, given by senior researchers, with the idea of giving you a more detailed insight to a particular topic within the realm of Operator Algebras. We are very happy to announce that this years speakers were:

Amine Marrakchi - Averaging in von Neumann algebras and applications

Given a group of automorphisms G of a von Neumann algebra M and an element x of M, when does the closed convex hull of the G-orbit of x contain a G-fixed point? This averaging problem is related to many deep questions in the theory of von Neumann algebras such as the classification of injective factors, Kadison's problem on maximal abelian algebras and Connes' bicentralizer conjecture. 

In this minicourse, I will introduce some old and new averaging techniques and I will present some applications.

Emily Peters - Diagrammatic methods in C* tensor categories

Without assuming any background in category theory, we will build up to a discussion of diagrammatic categories and C* structures in tensor categories.

Gábor Szabó - A glimpse into the classification of C*-algebras and group actions

This minicourse provides a relatively basic introduction to some of the core methods one needs when classifying either C*-algebras or group actions on C*-algebras. 

In the first part, we will cover Elliott intertwining, which is a technique to abstractly produce isomorphisms between C*-algebras via analytical means under suitable conditions. This leads to the idea that a desired functorial classification theorem can be deduced from so-called existence and uniqueness theorems (a slogan often repeated at conferences), which we shall endow with concrete meaning. We then direct our attention to finite group actions, which will be motivated by the fact that the Elliott intertwining machinery has a rather obvious dynamical analog in this context that requires almost no extra effort.

In the second part, I will present the basics behind the classification theory of finite group actions with the Rokhlin property, which is a dynamical regularity condition introduced by Izumi. We will discuss examples and how one can connect the elementary part of this classification theory to computable C*-algebraic invariants such as K-theory. If time permits, we may briefly discuss how to change the methodological framework in order to classify actions of infinite groups, along with a few model results that would be stated without proof.