top of page

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!):

 

 

Spring 2023:

1/12/2023- David Rose, University of North Carolina, Chapel Hill:

A Kirby color for Khovanov homology

 

In the context of quantum link invariants, a Kirby color is a linear combination of cabling patterns with the property that the resulting colored link polynomial is invariant under the second (handle slide) Kirby move. In familiar cases (e.g. Witten--Reshetikhin--Turaev), these invariants admit a renormalization that is invariant under the first (blow-up) Kirby move and thus yield invariants of closed, orientable 3-manifolds.

 

We will discuss a Kirby color for Khovanov homology, an ind-object in the annular Bar-Natan category (the monoidal category associated to the annulus in the Khovanov theory), which is equipped with a natural handle slide isomorphism. Functoriality properties of Khovanov homology imply that Kirby-colored Khovanov homology is invariant under the handle slide Kirby move. Using work of Manolescu--Neithalath, Kirby-colored Khovanov homology agrees with the Morrison--Walker--Wedrich skein lasagna invariant, thus is an invariant of the 4-manifold resulting from 2-handle additions along the corresponding link in the 3-sphere.

1/26/2023- Moritz Weber, Saarland University: Classification of easy quantum groups

Easy quantum groups form a class of compact quantum groups (in the sense of Woronowicz) whose representation categories can be described combinatorially by partitions of sets, similar to Temperley-Lieb algebras, Brauer diagrams, planar partitions or related objects. We will briefly introduce easy quantum groups and then survey its classification. We will also mention graph categories as defined by Mancinska-Roberson in order to describe the representation categories of quantum automorphism groups of graphs.

2/23/2023- Dylan Thurston, Indiana University, Bloomington: TBA

3/9/2023- Amrei Oswald, University of Washington: TBA

 

5/4/2023- Qing Zhang, Purdue University: TBA

 

bottom of page