# Quantum Algebra and Quantum Topology Seminar

When: Tuesday 1:50-2:50 PM

Where: Cockins Hall 240 (CH 240)

Organizer: Thomas Kerler

Administrator of this website: Yu Tsumura

News
1/23 Title and abstract of Yilong Wang's talk (1/23) were added.

Below is for Autumn 2017
12/3 Title and abstract of Matthew Harper's talk (12/5) were added.
10/2 Title and abstract of Yilong Wang's talk (10/3) were added.
9/25 Title and abstract of Christopher Schommer-Pries's talk (10/17) were added.
9/1 Title and abstract of Cody Armond's talk (9/5) were added.
8/21 Title and abstract of David Penney's talk (8/22) were added.

Below is for Spring 2017
5/10 Title and abstract of Richard Ng's talk on 5/25 were added.
4/11 Title and abstract of Sergey Lando's talk on 4/13 were added.
3/29 Title, abstract, references for Julia Plavnik's talk (4/4 Tuesday) were added.
3/21 Title and abstract of Diana Hubbard's talk on 3/30 were added.
2017
Below is 2016
12/11 Slides for Eric Rowell's talk were added.
11/17 Slides for Yilong Wang's talk were added.
11/14 Title, abstract, references for Yilong Wang's (11/17) talk were added.
11/11 Reference for Patrick Gilmer's talk (12/8) was added.
11/07 Title and abstract of David Penney's talk (11/10) were added.
11/06 References for Marcel Bischoff's talk were added.
11/04 Title and abstract of Patrick Gilmer's talk (12/1) were added.
11/01 References for Eric Rowell's talk were added.
10/31 Title and abstract of Eric Rowell's talk were added.
10/27 Title and abstract of Marcel Bischoff's talk were added.
10/13 Title and abstract of Alexei Davydov's talk were added.
10/4 Title and abstract of Alex Borland's talk were added.
9/19 Title and abstract of David Penney's talk were added.
9/7 Cody Armond's slides were added.
9/1

• Title and abstract of Cody Armond were added.
• Title and abstract of Noah Snyder were added.

8/31 Alexei Davydov's talk is scheduled on Oct. 27th.
8/30 David Penneys' talk has moved to Sep 22nd.
8/29 Title and abstract of Corey Jones's talk were added.

## Past Speakers

### 3/6/2018 Hans Wenzl (UCSD)

#### Abstract: Tensor categories whose fusion ring is isomorphic to the one of a spin group have a Z/2Z grading. The 0-part is known from the classification of orthogonal categories, assuming braiding. Its module action is then classified using a type B version of the so-called BMW algebra. This allows the reconstruction of the whole category.

Hans Wenzl's Website

### 10/24/2017 Marcel Bischoff (Ohio University)

#### Abstract: Metaplectic modular categories are modular tensor categories whose fusion rules are given by the Verlinde fusing rules of Spin(n) at level 2. One can generalize these fusion rules by replacing the cyclic group of order n with an arbitrary finite abelian group A. I will discuss the classification of modular categories with such fusion rules in the case that A is of odd order. I will also discuss the relation to twisted doubles of generalized dihedral groups.

Marcel Bischoff's website

### 10/17/2017 Christopher Schommer-Pries (University of Notre Dame)

#### Abstract: Fusion tensor categories arise in many areas of mathematics: as representation categories for finite quantum groups, certain Hopf algebras, and loop groups; as the "basic invariants" of subfactors of von Neumann algebras in the theory of operator algebras; and also in the study of conformal field theory. Fusion tensor categories have a rich and fascinating structure. The goal of this talk will be to describe how 3-dimensional topology and topological field theory allow this structure to be understood and explained. This is joint work with Christopher Douglas and Noah Snyder.

Christopher Schommer-Pries's website

### 10/3/2017 Yilong Wang

#### Abstract: In this talk, we will continue our discussion about the Jones polynomial following Peter Tingley's article. We will see how different choice of ribbon elements in $U_q(\mathfrak{sl}_2)$ will make a difference in sign in the construction of quantum invariants.

Reference: A minus sign that used to annoy me but now I know why it is there by Peter Tingley.

### 05/25/2017 Richard Ng

Louisiana State University Ng's website

### 04/13/2017 Sergey Lando

National Research University Higher School of Economics, Skolkovo Institute of Science and Technology (Sergey Lando's website)

### 04/04/2017 Julia Plavnik (Tuesday!!)

Texas A&M University
Julia Plavnik's website

### 03/30/2017 Diana Hubbard

The University of Michigan
Diana Hubbard's website

### 12/8/2016 Eric Rowell

Texas A&M University
Eric Rowell's website

#### References

Slides used in the talk.

Check out also Publications and Preprints of Eric C. Rowell

### 12/1/2016 Patrick Gilmer

Louisiana State University
Patrick Gilmer's website

#### Reference

An application of TQFT to modular representation theory
by Patrick M. Gilmer, Gregor Masbaum

### 11/17/2016 Yilong Wang

The Ohio State University

#### References

Slides used in the talk.

### 11/10/2016 David Penneys

The Ohio State University

#### Abstract: Fusion categories generalize the representation categories of quantum groups, and thus we think of fusion categories as objects which encode quantum symmetry. Recently, there has been a lot of interest in super fusion categories, which are enriched in super vector spaces. These objects are examples of tensor categories enriched in symmetric tensor categories. In this talk, I'll discuss an ongoing project with Morrison in which we study tensor categories enriched in a braided fusion category V, which is not assumed to be symmetric. We classify V-fusion categories in terms of oplax braided tensor functors from V to the centers of ordinary fusion categories. Under this correspondence, strong braided tensor functors correspond to V-complete V-fusion categories.

David Penneys' website

### 11/3/2016 Marcel Bischoff

Vanderbilt University
Marcel Bischoff's website

#### References

Part of the talk can be found in appendix B in
Generalized Orbifold Construction for Conformal Nets By Marcel Bischoff

The Prerequisites are in:

### 10/27/2016 Alexei Davydov

Ohio University

Alexei Davydov's website

### 10/6/2016 Alex Borland

The Ohio State University

### 9/29/2016 Noah Snyder

Indiana University

### 9/22/2016 David Penneys

The Ohio State University

#### Abstract:　 I'll first give an introduction to Jones' planar algebras, which are a useful tool for the construction and classification of subfactors and fusion categories. A folklore theorem says that sufficiently nice planar algebras are equivalent to pivotal tensor categories together with a distinguished choice of generating object. I'll then discuss joint work with Henriques and Tener, which generalizes the notion of a planar algebra in the category of vector spaces to a planar algebra internal to a modular tensor category $\color{black}C$. We generalize the above theorem, showing that planar algebras internal to $\color{black}C$ are in one-to-one correspondence with module tensor categories $\color{black}M$ for $\color{black}C$, a functor from $\color{black}C$ to the Drinfel'd center $\color{black}{Z(M)}$, and a distinguished object in $\color{black}M$ which generates $\color{black}M$ as a $\color{black}C$-module.

David Penneys' website

### 9/8/2016 Corey Jones

The Australian National University

### 9/1/2016 Cody Armond

The Ohio State University

#### Abstract: The colored Jones polynomial is a sequence of quantum knot invariant defined by the irreducible representations of sl(2). For alternating and adequate knots, it can be shown that the sequence of leading coefficients will stabilize, which allows us to define a power series invariant called the tail of the colored Jones polynomial. We will discuss the definition of this power series as well as techniques to compute it for certain large classes of knots, and it's relation to the all-A state graph of a particular diagram of the knot.

Slides used in the talk.

## Free Spots

### OSU holidays on Thursdays

The following dates are university holidays, so there will be no seminar on these days.