##### Department of Mathematics,

University of California San Diego

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### Math 269 - Combinatorics

## Ian Charlesworth

#### UCSD

## Combinatorics in Free Probability

##### Abstract:

Free probability was introduced in the 1980â€™s by Voiculescu, with the aim of studying von Neumann algebras by viewing them as non-commutative probability spaces, and this analogy has proved quite powerful in operator algebra theory. In the 1990â€™s, Speicher was able to describe free independence using cumulants constructed from the lattice of non-crossing partitions. In this talk we will give an introduction to free probability and outline the role the non-crossing cumulants have played in describing the theory. Time permitting we will also demonstrate some more recent applications of combinatorics to free probability, such as in describing bi-free probability, type B free probability, and boolean independence.

Jaques Verstraete and Brendon Rhoades

### October 17, 2017

### 4:00 PM

### AP&M 7321

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