##### Department of Mathematics,

University of California San Diego

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### MATH 288 - Probability & Statistics

## Ian Charlesworth

#### UCSD

## Bi-free probability and an approach to conjugate variables

##### Abstract:

Free entropy theory is an analogue of information theory in a non-commutative setting, which has had great applications to the examination of structural properties of von Neumann algebras. I will discuss some ongoing joint work with Paul Skoufranis to extend this approach to the setting of bi-free probability which attempts to study simultaneously ``left'' and ``right'' non-commutative variables. I will speak in particular of an approach to a bi-free Fisher information and bi-free conjugate variables -- analogues of Fisher's information measure and the score function of information theory. The focus will be on constructing these tools in the non-commutative setting, and time permitting, I will also mention some results such as bi-free Cramer-Rao and Stam inequalities, and some quirks of the bi-free setting which are not present in the free setting.

Host: Tianyi Zheng

### May 31, 2018

### 10:00 AM

### AP&M 6402

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