# Kyoto Operator Algebra Seminar

Organizers: Masaki IZUMI, Narutaka OZAWA, Yoshikata KIDA
Time and Location: 15:00 - 16:30 on Tuesday at RIMS 006
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 Spring/Summer

## 2014 Fall/Winter

 Sep. 08-10 RIMS 420 Recent developments in operator algebras (program) Sep. 30 15:00 - 16:30 RIMS 006 Mike Brannan (UIUC) Probabilistic aspects of (non-tracial) free orthogonal quantum groups In this talk, I will discuss the problem of computing moments (with respect to the Haar state) of the generators of Van Daele and Wang's $F$-deformed free orthogonal quantum groups $O^+_F$. The main technique here is a combinatorial Weingarten formula due to Banica and Collins. Using this technique, we show that as the quantum dimension'' of the quantum group tends to infinity, the rescaled generators converge in distribution to canonical generators of almost-periodic free Araki-Woods factors. Time-permitting, we will also discuss how the free orthogonal quantum groups $O^+_F$ can be realized as distributional symmetries of almost periodic free Araki-Woods factors. This talk is based on joint work with Kay Kirkpatrick. Oct. 06-10 Sci 3-127 Shigeru Yamagami (Nagoya) Intensive lecture course on quantum algebras Mon 15:00 - 17:00,  Tue 15:00 - 17:00,  Wed 10:00 - 12:00,  Thu 15:00 - 17:00,  Fri 10:00 - 12:00. Colloquium @ 3-110: Wed 15:00 - 16:00 Oct. 14 DT Seminar 15:00 - 16:30 Sci 6-609 Moon Duchin (Tufts University) Large-scale geometry of nilpotent groups Oct. 17 SGU Lecture 13:00 - 15:00 Sci 3-108 (Sci 3-305) Gennadi Kasparov (Vanderbilt University) Introduction to Index theory and KK-theory Every Friday from October 17 to November 28 from 13:00 to 15:00 at 3-108, except on October 24 and November 14 at 3-305. The course will contain the operator $K$-theory approach to the Atiyah-Singer index theorem. We will start with some classical examples of elliptic differential operators on compact smooth manifolds without boundary. This will naturally lead us to two special cases of $KK$-theory: $K$-cohomology and $K$-homology. $KK$-theory will be introduced gradually, as much as it is needed for index theory. Most examples will come from differential and pseudo-differential operators. Large part of technical results related with $KK$-theory will be given without proof: because time is limited, and also because we need $KK$-theory for this course only as a tool. Other technical tools include Clifford algebras and Dirac operators. Although all definitions will be given in the course, I advise the listeners to consult the book Spin geometry'' by H. B. Lawson and M.-L. Michelsohn on these issues. The main part of the course will contain a proof of the $K$-theoretic version of the Atiyah-Singer index theorem. The cohomological Atiyah-Singer index formula for compact manifolds will be obtained as a corollary. Various applications will be discussed as much as time allows. Recommended literature: 1. M. F. Atiyah, I. M. Singer: The index of elliptic operators'', I, III, Annals of Math., 87 (1968), 484-530, 546-604. 2. H. B. Lawson, M.-L. Michelsohn: Spin geometry'', Princeton Univ. Press, 1989. Oct. 21 15:00 - 16:30 RIMS 006 Yusuke Isono (Kyoto) Free independence in ultraproduct von Neumann algebras and applications We generalize Popa's free independence result for ultra products of $\mathrm{II}_1$ factors to the framework of type $\mathrm{III}$ factors with large centralizer algebras. Then we give two applications. First, we give a direct proof of stability under free product of QWEP for von Neumann algebras. Second, we give a new class of inclusions of von Neumann algebras with relative Dixmier property. This is a joint work with C. Houdayer. Oct. 28 15:00 - 17:00 RIMS 006 Narutaka Ozawa (Kyoto) The Furstenberg boundary and $\mathrm{C}^*$-simplicity I A (discrete) group $G$ is said to be $\mathrm{C}^*$-simple if the reduced group $\mathrm{C}^*$-algebra of it is simple. I will first explain Kalantar and Kennedy's characterization of $\mathrm{C}^*$-simplicity for a group $G$ in terms of its action on the maximal Furstenberg boundary. Then I will talk about my result with Breuillard, Kalantar, and Kennedy about examples and stable properties of $\mathrm{C}^*$-simple groups. Nov. 04 13:15 - 14:45 RIMS 006 Narutaka Ozawa (Kyoto) The Furstenberg boundary and $\mathrm{C}^*$-simplicity II 15:00 - 16:30 RIMS 006 Hiroshi Ando (Copenhagen) On the noncommutativity of the central sequence $\mathrm{C}^*$-algebra $F(A)$ We show that the central sequence $\mathrm{C}^*$-algebra of the free group $C_r^*(\mathbb{F}_n)\ (n\ge 2)$ is noncommutative, answering a question of Kirchberg in 2004. This is in contrast to the fact that the $\mathrm{W}^*$-central sequence algebra of the group von Neumann algebra $L(\mathbb{F}_n)$ is trivial. This is joint work with Eberhard Kirchberg. Nov. 11 Kyoto Prize 13:00 - 16:30 ICC Kyoto Edward Witten (IAS) Adventures in Physics and Math Nov. 18 15:00 - 16:30 RIMS 006 Takahiro Hasebe (Hokkaido) Extension of $q$-Fock space in terms of Coxeter group of type B A $q$-Fock space was introduced by Bozejko and Speicher in 1991. Its inner product contains a parameter $q$ and it interpolates the boson ($q=1$), fermion ($q=-1$) and full ($q=0$) Fock spaces. In this talk I will explain a further deformation by two parameters $(a,q)$ which come from Coxeter groups of type B. This is a joint work with Marek Bozejko and Wiktor Ejsmont. Nov. 29&30 Shirahama Kansai Operator Algebra Seminar Dec. 09 15:00 - 16:30 RIMS 006 Yoshikata Kida (Kyoto) OE and $\mathrm{W}^*$-superrigidity results for actions by surface braid groups We show that some natural subgroups of the mapping class group has rigidity in the title. Particularly I explain strategy for OE rigidity of strong type. This is based on my old work on mapping class groups. I will first briefly review mapping class groups and how their rigidity is obtained. This is a joint work with Ionut Chifan. Dec. 16 15:00 - 16:30 RIMS 006 Reiji Tomatsu (Hokkaido) Fullness of the core von Neumann algebra of free product factors I will talk about the fullness of the core von Neumann algebras of free product factors of type III$_1$ and present a characterization in terms of Connes' $\tau$-invariant. This is a joint work with Yoshimichi Ueda. Dec. 24-26 Hakusan Annual meeting on operator theory & operator algebra theory Jan. 06 15:00 - 16:30 RIMS 006 Sven Raum (RIMS/Münster) Character rigidity for lattices in higher rank groups I (after Creutz-Peterson, Peterson) A discrete group $G$ is called character rigid if every representation of $G$ on a Hilbert space generating a finite factor is either the left regular representation or generates a finite dimensional factor. Creutz-Peterson and Peterson proved that many lattices in Lie groups and their products with totally disconnected groups are character rigid. In this talk we review results of Creutz-Peterson proving character rigidity for lattices in products of certain property (T) Lie groups with totally disconnected Howe-Moore groups. We introduce necessary terminology and explain the strategy of proof. This will be set the precursor to understand Petersons result on character rigidity for lattices in higher rank semi-simple Lie groups. Jan. 13 15:00 - 16:30 RIMS 006 Sven Raum (RIMS/Münster) Character rigidity for lattices in higher rank groups II (after Creutz-Peterson, Peterson) Jan. 16 Prob Seminar 15:30 - 17:00 Sci 3-552 J L (kC) R蕪z̐ьÓT蕪zƂ̊֌W Jan. 20 15:00 - 16:30 RIMS 006 Rui Okayasu (Osaka Kyoiku) Haagerup approximation property and bimodules I try giving a characterization of Haagerup approximation property for arbitrary von Neumann algebra in terms of bimodules. Jan. 27 15:00 - 16:30 RIMS 006 Narutaka Ozawa (RIMS) Maximal amenable von Neumann algebras (after Boutonnet and Carderi arXiv:1411.4093) Feb. 02-04 RIMS 111 Classification of operator algebras and related topics (program) Mar. 09&10 Sci 3-127 SGU Mathematics Kickoff Meeting Mar. 12-18 SGU Lecture RIMS*** Gilles Pisier (TAMU) Grothendieck Inequality, Random matrices and Quantum Expanders Thu 15:30 - 17:00,  Fri 15:30 - 17:00,  Mon 10:30 - 12:00,  Tue 10:30 - 12:00,  Wed 10:30 - 12:00. Lecture 1: Grothendieck's inequality in the XXIst century In a famous 1956 paper, Grothendieck proved a fundamental inequality involving the scalar products of sets of unit vectors in Hilbert space, for which the value of the best constant $K_G$ (called the Grothendieck constant) is still not known. Surprisingly, there has been recently a surge of interest on this inequality in Computer Science, Quantum physics and Operator Algebra Theory. The first talk will survey some of these recent developments. Lecture 2: Non-commutative Grothendieck inequality Grothendieck conjectured a non-commutative version of his Fundamental theorem on the metric theory of tensor products", which was established by the author (1978) and Haagerup (1984). This gives a factorization of bounded bilinear forms on $C^*$-algebras. More recently, a new version was found describing a factorization for completely bounded bilinear forms on $C^*$-algebras, or on a special class of operator spaces called exact". We will review these results, due to the author and Shlyakhtenko (2002) and also Junge, Haagerup-Musat (2012) , Regev-Vidick (2014). Lecture 3: The importance of being exact The notion of an exact operator space (generalizing Kirchberg's notion for $C^*$-algebras) will be discussed in connection with versions of Grothendieck's inequality in Operator Space Theory. Random matrices (Gaussian or unitary) play an important role in this topic. Lectures 4 and 5: Quantum expanders Quantum expanders will be discussed with several recent applications to Operator Space Theory. They can be related to smooth" points on the analogue of the Euclidean unit sphere when scalars are replaced by $N\times N$-matrices. The exponential growth of quantum expanders generalizes a classical geometric fact on $n$-dimensional Hilbert space (corresponding to $N=1$). Miscellaneous applications will be presented: --to the growth of the number of irreducible components of certain group representations in the presence of a spectral gap, --to the metric entropy of the metric space of all $n$-dimensional normed spaces for the Banach-Mazur distance or its non-commutative (matricial) analogues, --to tensor products of $C^*$-algebras.

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