# Analysis Seminar

Wednesday, November 10, 2021 — 4:00 PM EST

Brent Nelson, Michigan State University

"Free Stein Dimension"

Let $A$ be a finitely generated *-algebra with a faithful tracial state $\tau$, and identify $A$ with its GNS representation on $L^2(A,\tau)$. The free Stein dimension of $(A,\tau)$ is the von Neumann dimension of a module spanned by derivations of the form $\delta\colon A\to L^2(A,\tau)$. Like other free probabilistic quantities, its value can reveal structural properties of the von Neuman algebra $A''$. One advantage of free Stein dimension is that it can be easily computed for many examples, including for certain dense *-subalgebras of the orthogonal free quantum group factors. In this talk, I will provide an introduction to free Stein dimension and demonstrate some computational techniques with potential applications to more general quantum groups. This is joint work with Ian Charlesworth.

This seminar will be held jointly online and in person:

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### May 2022

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