Events

Erik Seguin (University of Waterloo)

Minimality in noncommutative dynamics

In this talk, we discuss the notion of minimality for C*-dynamical systems. We show that the accepted definition is somewhat unsatisfactory as an extension of its commutative counterpart from both a topological dynamical and an operator algebraic perspective and present an alternative notion of an extension which rectifies these issues. We discuss various consequences of this alternative definition. 

MC 5403

Lilian Gardner (University of Waterloo)

The Chifan-Ioana-Kunnawalkam Elayavalli Lifting Lemma

The construction of a separable II_1 factor without property Gamma, and which is not elementarily equivalent to the free group factors requires a lifting lemma, for which if four orthogonal projections in an ultraproduct of II_1 factors are chosen to satisfy certain properties, then sequence representatives of each projection can be chosen to also satisfy the same properties. We go over the proof of this lifting lemma.

MC 5501

Ian Charlesworth (Cardiff University)

Mixtures of classical and free independence

\(\varepsilon\)-free probability was first introduced by Mlotkowski in the early 2000s to understand and model \(q\)-deformed Gaussian variables, which interpolate between the usual Gaussian distribution at q = 1 and the free semicircular distribution at q = 0. It describes an independence relation for tuples of algebras, some in free position and some in tensor position. A similar construction for groups (the graph product, which interpolates between the free product and the direct product) was introduced by Green in 1990, and extended to operator algebras by Caspers and Fima, independently recovering Mlotkowski's definitions. These objects have attracted quite a bit of attention over recent years, both from the viewpoint of non-commutative probability theory and in studying their operator algebraic properties directly. I will discuss the state of the art concerning \(\varepsilon\)-free independence and graph product von Neumann algebras, including work of others and some of my own. Particular focus will be given to my recent joint work with Jekel, where we are able to use a 1969 result of Cartier and Foata on the combinatorics of words as the key to describing the type I summands of a graph product of von Neumann algebras.

MC 5403

Kaleb Ruscitti (University of Waterloo)

Lilian Gardner (University of Waterloo)

The exotic II_1 factor

In https://arxiv.org/abs/2209.10645, Chifan Ioana and Kunnawalkam Elayavalli construct a separable II_1 factor without property Gamma and which is not elementarily equivalent to any II_1 factor with positive 1-bounded entropy (e.g. free group factors). We present the construction of this II_1 factor.

MC 5403