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Archive : Inverse Problems and Analysis

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David Penneys, Ohio State UniversityDavid Penneys, Ohio State UniversityEWG 336Title: Classifying small quantum symmetries <br><br> Abstract: Unitary fusion categories generalize the representation categories of quantum groups, and thus we say that fusion categories encode quantum symmetries. In order to represent unitary fusion categories as categories of Hilbert spaces, we are naturally led to von Neumann algebras and subfactors. Every unitary fusion category can be realized as a category of bimodules associated to a finite index subfactor, so we say that subfactors are universal hosts for quantum symmetries. In one sense, subfactors of small index are the simplest subfactors. I will discuss the small index subfactor classification program and the search for exotic examples of quantum symmetries.3/23/2018 2:00:00 PM3/23/2018 3:00:00 PMFalse
Dr. Ken Dykema, Texas A&M university Dr. Ken Dykema, Texas A&M university Ewing 336Title: Non-closure of a set of quantum correlations <br></br> Abstract: Several different models exist for quantum strategies for non-local games, (e.g., the graph coloring game). Different models correspond to different sets of correlation matrices. Open questions about these sets of correlation matrices remain, including some that are equivalent to Connes' Embedding Conjecture. One set of correlation matrices is the set of those arising from finite dimensional projections. The question of whether this set is always closed was solved in the negative by William Slofstra, in early 2017. <br></br> In this talk, we will briefly introduce the theory of quantum strategies for non-local games and the corresponding sets of correlation matrices, and we will describe the current state of knowledge about them. Then we will discuss a newer proof of Slofstra's result, which actually works for games with fewer inputs and outputs than Slofstra required. This latter result is joint work with Vern Paulsen and Jitendra Prakash. It relies on some very nice results about scalar multiples of the identity which are equal to sums of projections, due to Kruglyak, Rabanovich, Samoilenko. 3/14/2018 2:00:00 PM3/14/2018 3:00:00 PMFalse
Dr. Anna Skripka, University of New Mexico Dr. Anna Skripka, University of New Mexico Ewing 336Title:A uniqueness property of spectral sum approximations <br></br> Abstract: </br> We will discuss uniqueness of a nonlinear inverse problem arising in approximation of spectral sums. The main result asserts that Taylor approximations of a spectral sum of order greater than or equal to two have vanishing remainders for all monomials if and only if the respective perturbation is zero. This result complements non-uniqueness of the first order Taylor remainder. It is obtained by taking a spline based approach to Taylor remainders and also holds in a certain infinite dimensional setting. The talk is based on joint work with M. Zinchenko. 2/28/2018 3:00:00 PM2/28/2018 4:00:00 PMFalse
Dr. Der-Chen Chang, Georgetown UniversityDr. Der-Chen Chang, Georgetown UniversityEWG 336Title: On Heat kernel asymptotic expansions for sub-elliptic operators <br></br> Abstract: In this talk, we shall discuss the heat kernels for some sub-elliptic operators, especially the Heisenberg sub-Laplacaian and Grushin operators. Then we shall discuss small time asymptotic expansions and Li-Yau estimates for the eigenvalues of Dirichlet problem of these operators. 2/21/2018 3:00:00 PM2/21/2018 4:00:00 PMFalse

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