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
    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
    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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