# Kyoto Operator Algebra Seminar

Organizers: Benoit COLLINS, Masaki IZUMI, Narutaka OZAWA.
Time and Location: 15:00 - 16:30 on Tuesday at RIMS 206
Seminar Description: This seminar features both research and introductory talks on topics in Operator Algebra, Noncommutative Geometry, Ergodic Theory, and Group Theory of various kinds (geometric, measure theoretic, functional analytic, etc.). The talks are informal and take between an hour and an hour and a half.
Useful Tips: How to Give a Good Colloquium. Advice on Giving Talks (Upgrade). Myths.
Memento: 2011  2012  2013  2014

## 2015 Spring/Summer

 Apr. 04 15:00 - 18:00 RIMS 209 Roadmap Meeting Apr. 07 14:00 - 15:30 RIMS 206 Yuhei Suzuki (Tokyo) Construction of minimal skew products of amenable minimal dynamical systems We give a generalization of a result of Glasner and Weiss. This provides many new examples of amenable minimal dynamical systems of exact groups. We also study the pure infiniteness of the crossed products of minimal dynamical systems arising from this result. For this purpose, we introduce and study a notion of the finite filling property for etale groupoids, which generalizes a result of Jolissaint and Robertson. As an application, we show that for any connected closed topological manifold M, every countable non-amenable exact group admits an amenable minimal free dynamical system on the product of M and the Cantor set whose crossed product is a Kirchberg algebra. This extends a result of Rørdam and Sierakowski. Apr. 14 DT Seminar 15:00 - 16:30 Sci 6-609 Masato Mimura (Tohoku) New algebraization of Kazhdan and fixed point properties Apr. 14 16:45 - 18:15 RIMS 206 Seung-Hyeok Kye (Seoul) Various notions of positivity for bi-linear maps and applications to tri-partite entanglement We consider bi-linear analogues of $s$-positivity for linear maps. The dual objects of these notions can be described in terms of Schimdt ranks for tri-tensor products and Schmidt numbers for tri-partite quantum states. These tri-partite versions of Schmidt numbers cover various kinds of bi-separability, and so we may interpret witnesses for those in terms of bi-linear maps. We give concrete examples of witnesses for various kinds of three qubit entanglement. This is a co-work with Kyung Hoon Han. May 12 15:00 - 16:30 RIMS 206 Igor Klep (Auckland) Commuting Dilations and Linear Positivstellensätze Given a tuple $A=(A_1,...,A_g)$ of real symmetric matrices of the same size, the affine linear matrix polynomial $L(x):=I-\sum A_j x_j$ is a monic linear pencil. The solution set $S_L$ of the corresponding linear matrix inequality, consisting of those $x$ in ${\mathbb R}^g$ for which $L(x)$ is positive semidefinite (PsD), is called a spectrahedron. It is a convex semialgebraic subset of ${\mathbb R}^g$. We study the question whether inclusion holds between two spectrahedra. We identify a tractable relaxation of this problem by considering the inclusion problem for the corresponding free spectrahedra $D_L$. Here $D_L$ is the set of tuples $X=(X_1,...,X_g)$ of symmetric matrices (of the same size) for which $L(X):=I-\sum A_j \otimes X_j$ is PsD. We explain that any tuple $X$ of symmetric matrices in a bounded free spectrahedron $D_L$ dilates, up to a scale factor, to a tuple $T$ of commuting self-adjoint operators with joint spectrum in the corresponding spectrahedron $S_L$. The scale factor measures the extent that a positive map can fail to be completely positive. In the case when $S_L$ is the hypercube $[-1,1]^g$, we derive an analytical formula for this scale factor, which as a by-product gives new probabilistic results for the binomial and beta distributions. The talk is based on joint work with Bill Helton, Scott McCullough and Markus Schweighofer. May 26 15:00 - 16:30 RIMS 206 TBA TBA June 09 15:00 - 16:30 RIMS 206 TBA TBA June 30 15:00 - 16:30 RIMS 206 TBA TBA July ** 15:00 - 16:30 RIMS 206 TBA TBA Aug. 19-21 RIMS 111 Recent developments in operator algebras (program)

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