# Schedule of Talks, Abstracts

All talks will be held in the math department, SC 1308 (Stevenson Center, Building 1, room 1308). Talks will start at 9:30am on Saturday, 9/30, and end around 1pm on Sunday, 10/1.

## Schedule of Talks

Friday, 9/29/17
Ralph Kaufmann will speak in the Subfactor Seminar (4:10pm in SC 1432).
Saturday, 9/30/17
Talks start at 9:30am and are 50 minutes long.

Tobias Osborne
Coffee break
Zhengwei Liu

Lunch break

Talks start at 2pm and are 50 minutes long.

Terry Gannon
Birgit Kaufmann
Coffee break
Dylan Thurston

Beer & Pizza in SC 1425 (starts after Dylan’s talk)

Sunday, 10/1/17
Talks start at 9:30am and are 50 minutes long.

James Tener
Coffee break
Feng Xu
Simon Wood

End of workshop at around 1pm.

## Titles and Abstracts

Terry Gannon, University of Alberta
Significant sharpening of the Ocneanu-Schopieray bound for modular
invariants
Abstract: Modular invariant partition functions are the basic combinatorial
data describing bulk conformal field theories, module categories, extensions
of vertex operator algebras, etc. The first and most famous result in this
direction was the 1986 A-D-E classification of affine sl(2) modular
invariants; they are also known for affine sl(3) (mid 1990s). In the early
2000s, Ocneanu gave a bound for affine sl(2) modular invariants and
suggested that it generalizes to all other affine algebras. Recently,
Schopieray (following Ostrik) fleshed out the details for the three rank 2
algebras, and it is clear that his argument indeed generalizes to all affine
algebras. His bound grows exponentially with the number of roots, and is 3
million for sl(3) and around a google for E8. In this paper we use a
different method, obtaining a much sharper bound, which grows with the cube
of the rank. E.g. sl(3) has 38 bad levels, sl(9) has 1202,  and E8 has 12476
bad levels. Using the new bounds, the modular invariant classification can
be completed for all classical algebras up to rank 6 as well as G2.
Birgit Kaufmann, Purdue University
Bethe-Ansatz for an SU(3) Hecke quotient
Abstract: The Temperly-Lieb (TL) algebra is ubiquitous in mathematical
physics appearing for instance in statistical mechanics in the form of
$U_q(su(2))$ invariant spin chains and the theory of planar algebras.
The TL-algebra can be realized as a quotient of the Hecke algebra for
the A-Coxeter systems. There are other quotients of this Hecke algebra
which are also of interest in many situations. We will discuss a
particular integrable model that arises in physics in the context of
reaction-diffusion systems with several species of particles. This
model can also be viewed a $U_q(su(3))$ invariant spin chain. We
derive Bethe Ansatz equations and use them to find the dynamical
critical exponent in this integrable model. Furthermore there is an
interesting connection to a surface growth model governed by the KPZ
equation, which we will discuss if time permits.
Zhengwei Liu, Harvard University
From subfactors to quantum information and back
Abstract: We first talk about the applications of subfactor theory in
quantum information. Inspired by a question in quantum information, we
introduce surface algebras as an extension of planar algebras from the plane
to surfaces. As an application, we give a new proof of the Verlinde formula
for any modular tensor category (MTC) and any genus surface. We also prove
new identities for MTCs including the 6j symbol self-duality. The proof is
based on a recent result joint with Feng Xu, which identifies two different
Fourier dualities in subfactors and MTCs.
Tobias Osborne, University of Hannover
Tensor network representations of spacetime symmetries
Abstract: Tensor network models for spacetime have enjoyed considerable recent interest in physics. However, what exactly is a tensor network model for a given spacetime? Certainly we know one when we see one, e.g., the multiscale
entanglement renormalisation ansatz is understood to be a good model for a
(time slice of) anti de Sitter space. But there are still ambiguities if you
want to make things precise. In this talk I attempt to supply a
mathematician-friendly definition of a “tensor network representation of
spacetime”. I’ll argue that a tensor network model is a (projective) unitary
representation of the symmetry group of spacetime via tensor-network unitary
operators. Properties of these representations will be discussed and
connections to Jones’ unitary representations of Thompson’s group T will be
sketched.
James Tener, UC Santa Barbara
Geometry of conformal nets
Abstract: The category of representations of a two-dimensional chiral
conformal field theory is thought of as a braided tensor category, but in
fact it has quite a bit more structure. According to Graeme Segal, there
should be a tensor product operation for every complex pair of pants, and
indeed every complex cobordism should produce some operation on this
category. I will describe a construction of Segal CFTs from conformal nets
and a geometric picture underlying certain subfactors constructed from the
nets. This is joint work in progress with Andre Henriques.
Dylan Thurston, Indiana University
Quantum exceptional series
Simon Wood, Cardiff University
Classifying positive energy modules in conformal field theory
Abstract: When attempting to construct a conformal field theory from some
vertex operator algebra, a major first obstacle that needs to be overcome is
the classification of modules. In this talk I will show how free field
algebras and symmetric functions can be used to prove module classification
theorems for some important families of vertex operator algebras.
Feng Xu, UC Riverside
Triality, golden ratio and subfactors
Abstract: I will describe some interesting  examples of subfactors  and their symmetries motivated by reconstruction program.

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