Lunch break<\/em><\/p>\nTalks start at 2pm and are 50 minutes long.<\/p>\n
Terry Gannon<\/b>
\nBirgit Kaufmann<\/b>
\nCoffee break<\/em>
\nDylan Thurston<\/b><\/p>\nBeer & Pizza in SC 1425 (starts after Dylan’s talk)<\/em>\n<\/ul>\nSunday, 10\/1\/17<\/strong>
\nTalks start at 9:30am and are 50 minutes long.<\/p>\nJames Tener<\/b>
\nCoffee break<\/em>
\nFeng Xu<\/b>
\nSimon Wood<\/b><\/p>\nEnd of workshop at around 1pm.<\/em>\n<\/ul>\nTitles and Abstracts<\/h2>\nTerry Gannon, University of Alberta<\/strong>
\nSignificant sharpening of the Ocneanu-Schopieray bound for modular
\ninvariants<\/em><\/ul>\nAbstract: Modular invariant partition functions are the basic combinatorial
\ndata describing bulk conformal field theories, module categories, extensions
\nof vertex operator algebras, etc. The first and most famous result in this
\ndirection was the 1986 A-D-E classification of affine sl(2) modular
\ninvariants; they are also known for affine sl(3) (mid 1990s). In the early
\n2000s, Ocneanu gave a bound for affine sl(2) modular invariants and
\nsuggested that it generalizes to all other affine algebras. Recently,
\nSchopieray (following Ostrik) fleshed out the details for the three rank 2
\nalgebras, and it is clear that his argument indeed generalizes to all affine
\nalgebras. His bound grows exponentially with the number of roots, and is 3
\nmillion for sl(3) and around a google for E8. In this paper we use a
\ndifferent method, obtaining a much sharper bound, which grows with the cube
\nof the rank. E.g. sl(3) has 38 bad levels, sl(9) has 1202, \u00a0and E8 has 12476
\nbad levels. Using the new bounds, the modular invariant classification can
\nbe completed for all classical algebras up to rank 6 as well as G2.\n<\/ul>\nBirgit Kaufmann, Purdue University<\/strong>
\nBethe-Ansatz for an SU(3) Hecke quotient<\/em><\/ul>\nAbstract: The Temperly-Lieb (TL) algebra is ubiquitous in mathematical
\nphysics appearing for instance in statistical mechanics in the form of
\n$U_q(su(2))$ invariant spin chains and the theory of planar algebras.
\nThe TL-algebra can be realized as a quotient of the Hecke algebra for
\nthe A-Coxeter systems. There are other quotients of this Hecke algebra
\nwhich are also of interest in many situations. We will discuss a
\nparticular integrable model that arises in physics in the context of
\nreaction-diffusion systems with several species of particles. This
\nmodel can also be viewed a $U_q(su(3))$ invariant spin chain. We
\nderive Bethe Ansatz equations and use them to find the dynamical
\ncritical exponent in this integrable model. Furthermore there is an
\ninteresting connection to a surface growth model governed by the KPZ
\nequation, which we will discuss if time permits.<\/ul>\nZhengwei Liu, Harvard University<\/strong>
\nFrom subfactors to quantum information and back<\/em><\/ul>\nAbstract: We first talk about the applications of subfactor theory in
\nquantum information. Inspired by a question in quantum information, we
\nintroduce surface algebras as an extension of planar algebras from the plane
\nto surfaces. As an application, we give a new proof of the Verlinde formula
\nfor any modular tensor category (MTC) and any genus surface. We also prove
\nnew identities for MTCs including the 6j symbol self-duality. The proof is
\nbased on a recent result joint with Feng Xu, which identifies two different
\nFourier dualities in subfactors and MTCs.\u00a0<\/ul>\nTobias Osborne, University of Hannover<\/strong>
\nTensor network representations of spacetime symmetries<\/em><\/ul>\nAbstract: 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
\nentanglement renormalisation ansatz is understood to be a good model for a
\n(time slice of) anti de Sitter space. But there are still ambiguities if you
\nwant to make things precise. In this talk I attempt to supply a
\nmathematician-friendly definition of a “tensor network representation of
\nspacetime”. I’ll argue that a tensor network model is a (projective) unitary
\nrepresentation of the symmetry group of spacetime via tensor-network unitary
\noperators. Properties of these representations will be discussed and
\nconnections to Jones’ unitary representations of Thompson’s group T will be
\nsketched.<\/ul>\nJames Tener, UC Santa Barbara<\/strong>
\nGeometry of conformal nets<\/em><\/ul>\nAbstract: The category of representations of a two-dimensional chiral
\nconformal field theory is thought of as a braided tensor category, but in
\nfact it has quite a bit more structure. According to Graeme Segal, there
\nshould be a tensor product operation for every complex pair of pants, and
\nindeed every complex cobordism should produce some operation on this
\ncategory. I will describe a construction of Segal CFTs from conformal nets
\nand a geometric picture underlying certain subfactors constructed from the
\nnets. This is joint work in progress with Andre Henriques.<\/ul>\nDylan Thurston, Indiana University<\/strong>
\nQuantum exceptional series<\/em><\/ul>\nSimon Wood, Cardiff University<\/strong>
\nClassifying positive energy modules in conformal field theory<\/em><\/ul>\nAbstract: When attempting to construct a conformal field theory from some
\nvertex operator algebra, a major first obstacle that needs to be overcome is
\nthe classification of modules. In this talk I will show how free field
\nalgebras and symmetric functions can be used to prove module classification
\ntheorems for some important families of vertex operator algebras.<\/ul>\nFeng Xu, UC Riverside<\/strong>
\nTriality, golden ratio and subfactors<\/em><\/ul>\nAbstract: I will describe some interesting \u00a0examples of subfactors \u00a0and their symmetries motivated by reconstruction program.<\/ul>\n","protected":false},"excerpt":{"rendered":"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…<\/p>\n","protected":false},"author":4749,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[],"class_list":["post-54","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/my.dev.vanderbilt.edu\/shankssubfactors17\/wp-json\/wp\/v2\/pages\/54","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/my.dev.vanderbilt.edu\/shankssubfactors17\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/my.dev.vanderbilt.edu\/shankssubfactors17\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/my.dev.vanderbilt.edu\/shankssubfactors17\/wp-json\/wp\/v2\/users\/4749"}],"replies":[{"embeddable":true,"href":"https:\/\/my.dev.vanderbilt.edu\/shankssubfactors17\/wp-json\/wp\/v2\/comments?post=54"}],"version-history":[{"count":24,"href":"https:\/\/my.dev.vanderbilt.edu\/shankssubfactors17\/wp-json\/wp\/v2\/pages\/54\/revisions"}],"predecessor-version":[{"id":788,"href":"https:\/\/my.dev.vanderbilt.edu\/shankssubfactors17\/wp-json\/wp\/v2\/pages\/54\/revisions\/788"}],"wp:attachment":[{"href":"https:\/\/my.dev.vanderbilt.edu\/shankssubfactors17\/wp-json\/wp\/v2\/media?parent=54"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/my.dev.vanderbilt.edu\/shankssubfactors17\/wp-json\/wp\/v2\/tags?post=54"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}