Colloquium

Speaker: Dr. Dietmar Bisch (Vanderbilt University)

Title: Subfactors and Quantum Symmetries

Abstract: Francis Murray and John von Neumann discovered in 1936 an

intriguing algebra of operators on Hilbert space, which they called the

hyperfinite II_1 factor R. Vaughan Jones showed in 1983 that R has a very

rich theory of subfactors by defining a notion of index for a subfactor.

His work led to surprising mathematical structures, including Jones' knot

invariant and exotic tensor categories of subfactor representations.

Caceres and I constructed in a recent paper new hyperfinite subfactors

with minimal quantum symmetries. They arise from so-called commuting

squares, a quite fascinating configuration of multi-matrix algebras.

Our work leads to explicit examples of hyperfinite quantum operations

with distinct sets of intrinsic quantum symmetries.

I will explain these concepts and make the talk accessible to a general

mathematical audience.