Sep. 0810 
RIMS 420 
Recent developments in operator algebras
(program)


Sep. 30 
15:00  16:30 RIMS 006 
Mike Brannan (UIUC)
Probabilistic aspects of (nontracial) 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 almostperiodic free ArakiWoods factors. Timepermitting, we will also discuss how the free orthogonal quantum groups $O^+_F$ can be realized as distributional symmetries of almost periodic free ArakiWoods factors. This talk is based on joint work with Kay Kirkpatrick.


Oct. 0610 
Sci 3127 
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 @ 3110: Wed 15:00  16:00


Oct. 14 DT Seminar 
15:00  16:30 Sci 6609 
Moon Duchin (Tufts University)
Largescale geometry of nilpotent groups


Oct. 17 SGU Lecture 
13:00  15:00 Sci 3108 (Sci 3305) 
Gennadi Kasparov (Vanderbilt University)
Introduction to Index theory and KKtheory
Every Friday from October 17 to November 28 from 13:00 to 15:00 at 3108, except on October 24 and November 14 at 3305.
The course will contain the operator $K$theory approach to the AtiyahSinger 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 pseudodifferential 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 AtiyahSinger index theorem. The cohomological AtiyahSinger 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), 484530, 546604.
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. 2426 
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 CreutzPeterson, 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. CreutzPeterson 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 CreutzPeterson proving character rigidity for lattices in products of certain property (T) Lie groups with totally disconnected HoweMoore 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 semisimple Lie groups.


Jan. 13 
15:00  16:30 RIMS 006 
Sven Raum (RIMS/Münster)
Character rigidity for lattices in higher rank groups II (after CreutzPeterson, Peterson)


Jan. 16 Prob Seminar 
15:30  17:00 Sci 3552 
長谷部 高広 (北海道)
自由安定分布の性質および古典安定分布との関係


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. 0204 
RIMS 111 
Classification of operator algebras and related topics
(program)


Mar. 09&10 
Sci 3127 
SGU Mathematics Kickoff Meeting


Mar. 1218 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: Noncommutative Grothendieck inequality
Grothendieck conjectured a noncommutative 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, HaagerupMusat (2012) , RegevVidick (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 BanachMazur distance
or its noncommutative (matricial) analogues,
to tensor products of $C^*$algebras.

