University Quantum Symmetries Lectures
( UQSL )
This is an online seminar organized by Corey Jones, David Penneys, and Julia Plavnik. Topics of interest range widely over "quantum" mathematics, and include (but are certainly not limited to):

Tensor categories

Subfactors and operator algebras

Hopf algebras and quantum groups

Representation theory

Higher Categories

TQFT and low dimensional topology

Categorification

Topological phases of matter

Conformal field theory

Algebraic quantum field theory
We typically meet Thursdays every other week from 2:00 pm  3:00 pm, US Eastern Time Zone. If you would like to attend, please email Corey Jones at cormjones88@gmail.com to be added to the Google Group for announcements of abstracts and Zoom links.
Here's a link to our schedule from previous semesters.
Below is a list of currently scheduled talks for this semester (which is updated frequently!):
Fall 2022:
9/8/2022 Robert Laugwitz, University of Nottingham:
Relative Drinfeld centers and nonsemisimple modular tensor categories
A finitetensor category is modular if it is a ribbon category with trivial Müger center. This definition relaxes the semisimplicity assumption compared to the usual definition of a modular fusion category. I will explain how relative Drinfeld centers can provide examples of such nonsemisimple modular tensor categories. These examples can be realized as modules over braided Drinfeld doubles. This talk is based on joint work with Chelsea Walton and Guillermo Sanmarco.
9/22/2022 Julia Pevstova, University of Washington:
Representations of a small quantum group via half quantum flag variety.
I will try to explain the categorical formalism which allows to study representations of a small quantum group “fiberwise” – by passing to a family of Borels parametrized by the (usual) complete flag variety. Nonetheless, to define such a family and to formally take fibers we make heavy use of the halfquantum flag variety, a noncommutative space G/B_q. Motivation for constructing such a formalism comes from multiple directions: modular representation theory, tensortriangular geometry, geometric representation theory, and TQFT. This is joint work with Cris Negron.
10/6/2022 Thibault Décoppet, University of Oxford:
The Morita Theory of Fusion 2Categories
I will begin by reviewing the different characterizations of Morita equivalence between fusion 1categories, and how this is related to the notion of a finite semisimple 2category. Then, I will recall the definitions of fusion 2categories and separable algebras therein, as well as examine some examples. Finally, I will explain how to define Morita equivalences between fusion 2categories.
10/20/2022 Sarah Reznikoff, Kansas State University:
Regular ideals and regular inclusions
We examine the regular ideals of C*algebras, examining which properties are preserved under quotients by these as well as the relationship between the regular ideals of A and the regular ideals of B when B \subseteq A is a regular inclusion. This is joint work with Jonathan Brown, Adam Fuller, and David Pitts.
11/3/2022 Maissam Barkeshli, University of Maryland:
Defects and higher symmetries in (3+1)D topological phases of matter
(3+1)D topological phases of matter can host interesting classes of nontrivial topological defects of varying codimension, of which the wellknown point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays an important role both in the classification of phases of matter and the possible faulttolerant logical operations in quantum error correcting codes. In this talk I will discuss some recent progress in our understanding of the properties of invertible defects and higher group symmetries in (3+1)D topological phases of matter. Along the way I will review some progress over the past few years in characterizing topological phases of matter and their defects in low dimensions.
11/17/2022 TBA
12/1/2022 Hongdi Huang, Rice University