- Berkeley Talk: Distortion for Multifactor Inclusions
- SCU Talk: An Introduction to Free Probability

- Winter CMS meetings: Combinatorics of the bi-free Segal-Bargmann transform
- YMC*A: Free Stein Irregularity
- GPOTS: Free Stein Information

## Free Stein Dimension. A talk recorded at the

*Wales MPPM seminar*.Regularity questions in free probability ask what can be learned about a tracial von Neumann algebra from probabilistic-flavoured qualities of a set of generators. Broadly speaking there are two approaches — one based in microstates, one in free derivations — which with the failure of Connes Embedding are now known to be distinct. The non-microstates approach is not obstructed by non-embeddable variables, but can be more difficult to work with for other reasons. I will speak on recent work with Brent Nelson, where we introduce a quantity called the free Stein dimension, which measures how readily derivations may be defined on a collection of variables. I will spend some time placing it in the context of other non-microstates quantities, and sketch a proof of the exciting fact that free Stein dimension is a *-algebra invariant.

## Asymptotic ε-independence. A presentation recorded at the Banff International Research Station in October 2019 during the workshop

*Classification Problems in von Neumann Algebras*.I will discuss ε-independence, which is an interpolation of classical and free independence originally studied by Młotkowski and later by Speicher and Wysoczanski. To be ε-independent, a family of algebras in particular must satisfy pairwise classical or free independence relations prescribed by a $\{0, 1\}$-matrix ε, as well as more complicated higher order relations. I will discuss how matrix models for this independence may be constructed in a suitably-chosen tensor product of matrix algebras. This is joint work with Benoît Collins.

## Free Stein Information. A presentation recorded at the Fields Institute in February 2019 during the

*Southern Ontario Operator Algebras Seminar*.I will speak on recent joint work with Brent Nelson, where we introduce a free probabilistic regularity quantity we call the free Stein information. The free Stein information measures in a certain sense how close a system of variables is to admitting conjugate variables in the sense of Voiculescu. I will discuss some properties of the free Stein information and how it relates to other common regularity conditions.

## An alternating moment condition and liberation for bi-freeness. A presentation recorded at the Banff International Research Station in December 2016 during the workshop

*Analytic Versus Combinatorial in Free Probability*.Bi-free probability is a generalization of free probability to study pairs of left and right faces in a non-commutative probability space. In this talk, I will demonstrate a characterization of bi-free independence inspired by the "vanishing of alternating centred moments" condition from free probability. I will also show how these ideas can be used to introduce a bi-free unitary Brownian motion and a liberation process which asymptotically creates bi-free independence.

- Connes Embedding Proglem/$MIP^*=RE$ reading group at UC Berkeley, Winter 2020.
- Joint Mathematics Meetings AMS Special Session on Advances in Operator Algebras. January 17, 2020 in Denver. Co-organized with Brent Nelson, Sarah Reznikoff, and Lauren Ruth.
- Joint Mathematics Meetings AMS Special Session: Advances in Operator Algebras. January 12-13, 2018 in San Diego. Co-organized with Marcel Bischoff, Brent Nelson, and Sarah Reznikoff.
- Trimester Junior Seminar during the 2016 von Neumann Algebras Trimester of the Hausdorff Research Institute for Mathematics, Universität Bonn.