**A Fourier cousin of the Birman-Murakami-Wenzl algebra, ,**at

**Harvard**, Wednesday, February 15, 2017

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Yau's geometry seminar

Mathematical Physics seminar

Abstract: In joint work with Arthur Jaffe and Alex Wozniakowski, we introduce a quon 3D picture language for quantum information using charged strings and 3-manifolds. Our 3D topological protocol for quantum teleportation have a piece wise identification with the algebraic circuit of Bennett et al. The relations of bi-Frobenius algebras, wildly used in tensor network, become...

Read more about Quon 3D language for quantum informationWorkshop on tensor networks and related problems

Abstract:

We give a topological simulation for tensor networks that we call the {\it two-string model}. In this approach we give a new way to design protocols, and we discover a new multipartite quantum communication protocol. We introduce the notion of topologically compressed transformations. Our new protocol can implement multiple, non-local compressed transformations among multi-parties using one multipartite resource state.

Subfactors and Mathematical Physics: Vaughan Jones (TSIMF)

Abstract:

The representation theory of a conformal net is a unitary modular tensor category (UMTC). It is captured by the bimodule category of the Jones-Wassermann subfactor. In joint work with Feng Xu, we construct multi-interval Jones-Wassermann subfactors for unitary modular tensor categories. We prove that these subfactors are self-dual. It generalizes the self-duality of finite abelian groups to a great extent and we call it modular self-duality.

Furthermore, we introduce a 2D anionic lattice...

Read more about Jones-Wassermann subfactors for modular tensor categoriesAbstract: In this talk, we will introduce a new type of Schur-Weyl duality that relates the representation theory of a paramterized algebra and a family of quantum subgroups. Feng Xu first constructed this family of quantum subgroups through conformal inclusions. The parameterized algebra was discovered in the classification of Yang-Baxter relation planar algebras, and constructed using skein theory. It turns out to be the centralizer algebra of this family of quantum subgroups. We give a closed-form expression for the quantum dimension of irreducible representations, in terms of Young...

Read more about Title: A new type of Schur-Weyl duality

NCG seminar

Abstract: In recent work joint with Chunlan Jiang and Jinsong Wu, we studied the Fourier analysis on finite index subfactors. We will talk about Hausdorff-Young inequality, Young's inequality, uncertainty principles, and sum set estimates. We give characterizations of the extremizers of these inequalities. These characterizations are new on the dual of a finite group.

Workshop on Subfactor theory, quantum field theory, and quantum information

Abstract: This work is joint with Arthur Jaffe and Alex Wozniakowski. We introduce a new diagrammatic approach to quantum information, that we call holographic software. Our new approach is a small modification of previous diagrammatic approaches, yet our small change leads to a great deal of new understanding and to a large number of new insights and motivation. Its application leads us to new protocols, designed in a "topological" way.

Mathematical Physics seminar

Mathematical Physics seminar

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