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 from 3:00 pm  4:00 pm (Eastern Time Zone). If you would like to attend, please email Corey Jones at to be added to the Google Group for weekly 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!):
Spring 2021:
1/14/2021 Michael Brannan, Texas A&M University:
Quantum graphs and quantum CuntzKrieger algebras.
I will give a light introduction to the theory of quantum graphs and some related operator algebraic constructions. Quantum graphs are generalizations of directed graphs within the framework of noncommutative geometry, and they arise naturally in a surprising variety of areas including quantum information theory, representation theory, and in the theory of nonlocal games. I will review the wellknown construction of CuntzKrieger C*algebras from ordinary graphs and explain how one can generalize this construction to the setting of quantum graphs. Time permitting, I will also explain how quantum symmetries of quantum graphs can be used to shed some light on the structure of quantum CuntzKrieger algebras. (This is joint work with Kari Eifler, Christian Voigt, and Moritz Weber.)
1/21/2021 No talk this week (rescheduled for 3/4/2021).
1/28/2021 Victor Ostrik, University of Oregon:
Two dimensional topological field theories and partial fractions.
This talk is based on joint work with M.Khovanov and Y.Kononov. By evaluating a topological field theory in dimension 2 on surfaces of genus 0,1,2 etc we get a sequence. We investigate which sequences occur in this way depending on the assumptions on the target category.
2/4/2021 Georgia Benkart, University of Wisconsin  Madison:
Fusion rules for Hopf algebras.
The McKay matrix M_V records the result of tensoring the simple modules with a finitedimensional module V. In the case of finite groups, the eigenvectors for M_V are the columns of the character table, and the eigenvalues come from evaluating the character of V on conjugacy class representatives. In this talk, we will explore what can be said about such eigenvectors when the McKay matrix is determined by modules for a finitedimensional Hopf algebra. The quantum group u_q(sl_2), where q is a root of unity, provides an interesting example.
2/11/2021 (TALK AT 2PM US EASTERN) Xie Chen, California Institute of Technology:
Foliation structure in fracton models.
Fracton models are characterized by an exponentially increasing ground state degeneracy and point excitations with limited motion. In this talk, I will focus on a prototypical 3D fracton model  the Xcube model  and discuss how its ground state degeneracy can be understood from a foliation structure in the model. In particular, we show that there are hidden 2D topological layers in the 3D bulk. To calculate the ground state degeneracy, we can remove the layers until a minimal structure is reached. The ground state degeneracy comes from the combination of the degeneracy of the foliation layers and that associated with the minimal structure. We discuss explicitly how this works for Xcube model with periodic boundary condition, open boundary condition, as well as in the presence of screw dislocation defects.
2/18/2021 Theo JohnsonFreyd, Dalhousie University/Perimeter Institute:
Condensations and Components.
The 1categorical Schur's lemma, which says that a nonzero morphism between simple objects is an isomorphism, fails for semisimple ncategories when n≥2. Rather, when two simple objects are related by a nonzero morphism, they each arise as a condensation descendant of the other. Because of this, for many purposes the natural ncategorical version of "set of simple objects" is the set of components: the set of simples modulo condensation descent. I will explain this phenomenon and describe some conjectures, including conjectures about "higher categorical Smatrices" and, time permitting, about the image of the jhomomorphism in the homotopy groups of spheres.
2/25/2021 Noah Snyder, Indiana University, Bloomington:
Demystifying subfactor techniques for constructing tensor categories
The primary goal of this talk is to explain two techniques used for constructing tensor categories that were developed among the subfactor community by AsaedaHaagerup and JonesPeters in purely tensor categorical terms. The secondary goal is to explain how these techniques generalize using module categories. This talk is based on a part of our Extended Haagerup paper with GrossmanMorrisonPenneysPeters (which builds on work of De CommerYamashita) and on work in progress with PenneysPeters.
3/4/2021 Andy Manion, University of Southern California:
Higher representations and cornered Floer homology.
I will discuss recent work with Raphael Rouquier, focusing on a higher tensor product operation for 2representations of Khovanov's categorification of U(gl(11)^+), examples of such 2representations that arise as strands algebras in bordered and cornered Heegaard Floer homology, and a tensorproductbased gluing formula for these 2representations expanding on work of DouglasManolescu.
3/18/2021 Zhenghan Wang, University of California Santa Barbara: TBA
3/25/2021 Eric Rowell, Texas A&M University: TBA
4/15/2021 Claudia Scheimbauer, Technische Universität München: TBA
4/22/2021 Radmila Sazdanovic, North Carolina State University: TBA
4/29/2021 Emily Riehl, Johns Hopkins University: TBA