# 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  2016

## 2016 Fall/Winter

 September 05-09 KTGU Lecture Sci 3-127 Sorin Popa (UCLA/Kyoto) Paving over arbitrary MASAs in von Neumann algebras 05(M) 15:00 - 17:00,  06(T) 15:00 - 17:00,  07(W) 15:00 - 17:00,  08(T) 15:00 - 17:00,  09(F) 15:00 - 17:00. Motivated by an intriguing claim in Dirac's 1947 book on "Quantum Mechanics", Kadison and Singer have asked the question of whether any pure state on the diagonal maximal abelian subalgebra (MASA) $D$ of $B(H)$ extends to a unique state on $B(H)$. They also showed that this unique pure state extension property is equivalent to norm paving over $D$ for operators in $B(H)$. The Kadison-Singer paving problem has been recently solved in the affirmative by Marcus--Spielman--Srivastava. In these lectures, we will introduce a general paving property for a MASA $A$ in a von Neumann factor $M$, called so-paving, involving approximation in the so-topology, rather than in norm, but which coincides with norm-paving in the case $D\subset B(H)$. We conjecture that so-paving holds true for any MASA in any factor. We check the conjecture in many cases, including singular and regular MASAs in hyperfine factors. Related problems will be discussed. Sep. 12-14 RIMS 420 Recent developments in operator algebras (program) Oct. 09-11 Maebashi Annual meeting on operator theory & operator algebra theory Oct 18 15:00 - 16:30 RIMS 206 Yusuke Isono (RIMS) Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors Let $M$ be a type $\mathrm{III}$ factor associated with a free (unitary or orthogonal) quantum group. We prove that for any factor $B$, the tensor product of $M$ and $B$ has no Cartan subalgebras. The main ingredient of the proof is a generalization of Ozawa--Popa and Popa--Vaes's weakly compact action at the level of the continuous core. We study it by using an operator valued weight to $B$ and the central weak amenability of $M$. Oct 25 15:00 - 16:30 RIMS 206 Koichi Shimada (Kyoto) Maximal amenability of the generator subalgebra in q-Gaussian von Neumann algebras We give explicit examples of maximal amenable von Neumann subalgebras of the $q$-Gaussian von Neumann algebras. More precisely, the generator subalgebra is maximal amenable inside the $q$-Gaussian algebras for real numbers $q$ with $|q|<1/9$. We would like to show this based on Popa's theory. In order to achieve this, we construct a Riesz basis in the spirit of Radulescu. This is a joint work with Sandeepan Parekh and Chenxu Wen. Nov 01 15:00 - 16:30 RIMS 206 Ivan Ip (Kyoto) Positive representations: a bridge between Drinfeld-Jimbo quantum groups and C*-algebra The finite dimensional representation theory of Drinfeld-Jimbo quantum group is well-known for representation theorist, and many applications have been discovered in the last 30 years. However, the non-compact case is a lot more complicated and much less is known. The notion of "positive representations" was introduced in a joint work with I. Frenkel to study the representation theory of split real quantum groups, which involves representations by unbounded operators. In this talk, I will give some motivations for such representation theory, and explain how the techniques from C*-algebra allow us to study the harmonic analysis and braiding structure of split real quantum groups. Nov 29 15:00 - 16:30 RIMS 206 Yuki Arano (Tokyo) TBA tba Dec 06 15:00 - 16:30 RIMS 206 Zhigang Bao (Hong Kong) Local law of addition of random matrices The question of how to describe the possible eigenvalues of the sum of two general Hermitian matrices dates back to Weyl. A randomized version of this question can give us a "deterministic" answer. Specifically, when two large-dimensional matrices are in general position in the sense that one of them is conjugated by a random Haar unitary matrix, the eigenvalue distribution of their sum is asymptotically given by the free convolution of the respective eigenvalue distributions. This result was obtained by Voiculescu on the macroscopic scale. In this talk, we show that this law also holds in a microscopic scale. This allows us to get an optional convergence rate for Voiculescu's result. Dec 13 15:00 - 16:30 RIMS 206 Raphael Ponge (Seoul) TBA tba Dec 20 15:00 - 16:30 RIMS 206 Yosuke Kubota (Tokyo) TBA tba Jan 10 15:00 - 16:30 RIMS 206 tba ( ) TBA tba Jan 17 15:00 - 16:30 RIMS 206 tba ( ) TBA tba

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