Probabilistic Operator Algebra Seminar: Type B Free Probability

Seminar | October 9 | 3:45-5:45 p.m. | 748 Evans Hall

 Ian Charlesworth, NSF Postdoctoral Fellow UC Berkeley

 Department of Mathematics

The lattice of non-crossing partitions plays a crucial role in free probability, giving rise to the free cumulants introduced by Roland Speicher. In addition to their combinatorial description, the non-crossing partitions can be realized as arising from the Coxeter groups of Type A. Reiner used this analogy to introduce the non-crossing partitions of Type B, which raises the question: what do these correspond to on the non-commutative probability side ? It turns out that the Type B theory leads to a kind of infinitesimal free independence. In this expository talk, we will present these ideas and discuss (briefly) how they can be applied to understand finite rank perturbations of random matrices.