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 non-semisimple modular tensor categories

A finite-tensor 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 non-semisimple 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 “fiber-wise” – 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 half-quantum flag variety, a non-commutative space G/B_q. Motivation for constructing such a formalism comes from multiple directions: modular representation theory, tensor-triangular 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 2-Categories

I will begin by reviewing the different characterizations of Morita equivalence between fusion 1-categories, and how this is related to the notion of a finite semisimple 2-category. Then, I will recall the definitions of fusion 2-categories and separable algebras therein, as well as examine some examples. Finally, I will explain how to define Morita equivalences between fusion 2-categories.

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 non-trivial topological defects of varying codimension, of which the well-known 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 fault-tolerant 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