Events for 01/30/2018 from all calendars

Linear Analysis Seminar

Time: 2:00PM - 3:00PM

Location: BLOC 220

Speaker: Dave Penneys, Ohio State

Title: Standard invariants for discrete subfactors

Abstract: The standard invariant of a finite index II_1 subfactor is a $\lambda$-lattice and forms a planar algebra. In turn, the planar algebra formalism has been helpful in constructing and classifying subfactors, as well as studying analytic properties. In joint work with Corey Jones, we give a well-behaved notion of the standard invariant of an extremal irreducible discrete subfactor $N\subset M$, where $N$ is type II_1 and $M$ is an arbitrary factor. We also get a subfactor reconstruction theorem. This generalizes the standard invariant for finite index subfactors to a natural class of infinite index subfactors. Particular examples include the symmetric enveloping inclusion and examples coming from discrete quantum groups.

Algebra and Combinatorics Seminar

Time: 4:00PM - 4:50PM

Location: BLOC 220

Speaker: Davis Penneys, The Ohio State University

Title: Exotic fusion categories: EH3 exists!

Abstract: Fusion categories generalize the representation categories of (quantum) groups, and we think of them as objects which encode quantum symmetry. All currently known fusion categories fit into 4 families: those coming from groups, those coming from quantum groups, quadratic categories, and those related to the extended Haagerup (EH) subfactor. First, I'll explain what I mean by the preceding sentence. We'll then discuss the extended Haagerup subfactor, along with the newly constructed EH3 fusion category (in joint work with Grossman, Izumi, Morrison, Peters, and Snyder), and the possibility of the existence of EH4.