April 03 
1:00  1:50 RIMS 204 
Narutaka Ozawa (RIMS)
Some useful but not welldocumented facts about tracial states on $\mathrm{C}^*$algebras
I will present some useful but not welldocumented facts about tracial states on $\mathrm{C}^*$algebras, and mention related open problems.


2:00  2:50 RIMS 204 
Hiroshi Ando (IHES)
Ultraproducts, QWEP von Neumann algebras and EffrosMarechal Topology
Haagerup and Winslow studied topological properties of the Polish space $\mathrm{vN}(H)$ of von Neumann algebras acting on the separable infinitedimensional Hilbert space $H$. Motivated by the work of Effros, this topology was introduced by Marechal. Among other interesting results, they proved that Kirhchberg's QWEP conjecture is equivalent to the assertion that the set ${\cal F}_{\mathrm{inj}}$ of injective factors on $H$ is dense in $\mathrm{vN}(H)$, and moreover a $\mathrm{II}_1$ factor $M$ on $H$ is $R^{\omega}$embeddable if and only if $M$ is a limit of a sequence of injective factors. Based on the work of HaagerupWinslow and the recent work of the speaker and Haagerup on ultraproducts, we will give new characterizations of QWEP von Neumann algebras.
This is a joint work with Uffe Haagerup and Carl Winslow (University of Copenhagen).


April 17 Colloquium 
4:30  5:30 MATH 110 
Yasuhiko Sato (Kyoto)
A characterization of classifiable nuclear $\mathrm{C}^*$algebras


April 24 
2:40  5:30 RIMS 420 
Enlarged Colloquium


May 15 
2:30  4:00 RIMS 204 
Yuhei Suzuki (Tokyo/RIMS)
On Quasidiagonal Representations of Nilpotent Groups (after Caleb Eckhardt)
Recently, Eckhardt has shown the full group $\mathrm{C}^*$algebras of discrete nilpotent groups are strongly quasidiagonal. In other words, any nilpotent subgroup of the unitary group on a Hilbert space is quasidiagonal. In this talk, I will give a slightly different proof from Eckhardt's one, which uses less knowledges about nilpotent groups.


May 29 
2:30  4:00 RIMS 204 
Masato Mimura (Tohoku)
多分割等周定数，エクスパンダー族と有限ケーリーグラフ
Multiway isoperimetries, expanders, and Cayley graphs
有限正則グラフ $G$ の（通常の）等周定数 $h_2(G)$ とは，グラフの頂点集合 $V$ の（空でない） $2$ 分割 $(A_1,A_2)$ を動かすとき， $A_i$の辺境界$$ を $A_i$ で割った量の $i=1,2$ での最大値の分割での最小値をとることで定義される．$2\le n\le V$ なる整数 $n$ をとるとき，グラフの頂点集合の（空でない）$n$ 分割で同様のことを考えることで，$G$ の $n$ 分割等周定数 $h_n(G)$ が定義される．$h_n(G)$ は $G$ のラプラス作用素の第 $n$ 固有値（$0$ を第 $1$ 固有値とする）$\lambda_n(G)$ と関連することが知られており，「チーガー型の不等式」と呼ばれている（$n=2$ のときは AlonV. Milman の著名な結果, 一般の場合は LeeGharanTrevisan による最近の結果による）．
$h_n(G)$ は $n$ について単調非減少だが，一般に $h_{n+1}(G)$ は $h_n(G)$ に比べいくらでも大きくなりうる．藤原耕二は，“グラフ $G$ が連結ケーリーグラフの場合に $h_{n+1}$ と $h_n$ の値の間には非自明な関係があるのではないか”，という問題を提起した．本講演では，この藤原耕二の問題の，講演者による定量的な解決をお話ししたい．講演者の結果から，任意の $n\geq2$ に対し，有限連結ケーリーグラフの列 $\lbrace G_m\rbrace_m$ において「$\inf_m h_n(G_m)$ が正である」ことと「$\inf_m h_2(G_m)$ が正である」ことの同値性が従う．また，有限な頂点推移的なグラフ $G$ と $n\geq2$ に対して，「$h_n(G)$ と $h_{n+1}(G)$ の間に（定量的な）ギャップがあるときには $G$ が（$n$ に依る形で記述できる）ある種の対称性をもつ」ことも明らかになった．
For a finite regular graph $G$, the (usual) isoperimetric constant $h_2(G)$ is defined as the minimum among nonempty decompositions $(A_1,A_2)$ of the vertex set $V$ of the maximum among $i=1,2$ of the ratio $$the edge boundary of $A_i/A_i$. For $n$ between $2$ and $V$, the $n$way isoperimetric constant $h_n(G)$ of $G$ is defined in terms of nonempty decomposiitons $(A_1,..., A_n)$ of $V$. Cheegertype inequalities, which relate $h_n(G)$ to the $n$th eigenvalue $\lambda_n(G)$ of the combinatorial Laplacian, are known: for $n=2$, this is a wellknown result of Alon and V. Milman, and for general $n$ this is a recent result of LeeGharanTrevisan.
$h_n(G)$ is nondecreasing on $n$, and in general $h_{n+1}(G)$ can be arbitrarily bigger than $h_n(G)$. Koji Fujiwara asks whether there exists any nontrivial relation between the values of $h_{n+1}(G)$ and $h_n(G)$ for finite connected Cayley graphs $G$. In this talk, the answer to this question by the speaker shall be presented. This unversal inequality provides with a corollary that for $n>2$ and for a sequence of finite connected Cayley graphs $\lbrace G_m\rbrace_m$, "$\inf_m h_n(G_m)>0$" in fact implies "$\inf_m h_2(G_m)>0$." Furthermore, it is shown that for a finite vertex transitive graph $G$ and $n>1$, an (explicitly stated) numerical gap between $h_{n+1}(G)$ and $h_n(G)$ implies a certain symmmetry (subscribed in terms of $n$) of the graph $G$.


June 08 
Osaka 
Kansai Operator Algebra Seminar


June 19 Colloquium 
4:30  5:30 MATH 110 
Yoshifumi Matsuda (Kyoto)
Rotation number and actions of the modular group on the circle


July 10 
2:30  4:00 RIMS 204 
Raphaël Ponge (Seoul)
Noncommutative geometry and conformal geometry
In this talk we shall report on a program of using the recent framework of twisted spectral triples to study conformal geometry from a noncommutative geometric perspective. One result is a local index formula in conformal geometry taking into account the action of the group of conformal diffeomorphisms. Another result is a version of VafaWitten's inequality for twisted spectral triples. Geometric applications include a version of VafaWitten's inequality in conformal geometry. There are also noncommutative versions for spectral triples over noncommutative tori and duals of discrete cocompact subgroups of semisimple Lie groups satisfying the BaumConnes conjecture. (This is joint work with Hang Wang.)


July 1619 
RIMS 420 
Geometric Group Theory  Kyoto 2013


July 22 
4:00  5:30 RIMS 109 
Raman Srinivasan (Chennai)
Noncocycleconjugate $E_0$semigroups on nontypeI factors


July 30 
3:00  4:30 Sci 6609 
Andrzej Żuk (Paris)
Expanders


Aug. 02 
1:00  2:30 MATH 305 
Tullio G. CeccheriniSilberstein (U. Sannio)
Cellular automata and groups
The purpose of this talk is to overview the theory of cellular automata on groups focusing on the Garden of Eden Theorem for cellular automata over amenable groups and Gottschalk's surjunctivity problem. This includes a presentation of a few examples of cellular automata (including Conway's Game of Life) and a discussion of the notions of amenability and soficity (due to GromovWeiss), and of the relation between surjunctivity and Kaplansky's conjecture on stable finiteness of group rings. The talk, completely selfcontained, addresses to a wide audience, including graduate students, interested in dynamical systems, group theory, operator algebras and ring theory, and theoretical computer science.


Sept. 1113 
RIMS 420 
Recent Progress in Operator Algebras (program)


Oct. 08 Tuesday 
16:30  18:00 RIMS 206 
Yuhei Suzuki (Tokyo/RIMS)
Amenable minimal Cantor systems of free groups arising from diagonal actions
G. A. Elliott and A. Sierakowski have constructed an amenable minimal Cantor system of free groups whose $K_0$group vanishes. In particular this is distinguished from the boundary action by $K$theory. In this talk we show every (f.g., noncommutative) free group admits continuum many amenable minimal Cantor systems whose crossed products are mutually nonisomorphic Kirchberg algebras with UCT by a different approach from that of ElliottSierakowski. The $K$theory of these Cantor systems are also determined explicitly.


Oct. 2128 
MATH 127 
Intensive Course by Hideki Kosaki (Kyushu)


Oct. 2128 
MATH 108 
Intensive Course by Shinichi Oguni (Ehime)


Oct. 23 Colloquium 
MATH 110 
Shinichi Oguni (Ehime)
The coarse BaumConnes conjecture for relatively hyperbolic groups


Oct. 29 Tuesday 
16:30  18:00 RIMS 206 
Pierre Fima (Paris 7/Tokyo)
Amenable, transitive and faithful actions of groups acting on trees
We study under which condition an amalgamated free product or an HNNextension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups admit an amenable and almost free action with infinite orbits (e.g. virtually free groups or infinite amenable groups). Our result relies on the Baire category Theorem. We extend the result to groups acting on trees.


Nov. 0608 
RIMS 110 
Operator monotone functions and related topics


Nov. 12 Tuesday 
16:30  18:00 RIMS 206 
Yusuke Isono (Tokyo)
Some prime factorization results for free quantum group factors
Ozawa and Popa proved some unique factorization properties for tensor products of free group factors. Roughly speaking, it means such a tensor product "remembers" each tensor component. In this seminar, we study similar factorization results for free quantum group factors. In the $\mathrm{II}_1$ factor case, we can follow OzawaPopa's method for free group factors. In the general case, we use continuous cores. More precisely, we observe a condition (AO) type phenomena for cores of the tensor products and then deduce some weak factorization properties.


Nov. 13 Enlarged Colloquium 
14:40  15:40 & 16:30  17:30 MATH 110 
Benoit Collins (Ottawa/Tohoku)
Free probability and quantum information theory
Kenji Fukaya (Stony Brook)
仮想チェインの方法の現状


Nov. 1617 
RIMS 
Takagi Lectures


Dec. 04 
13:30  14:40 & 14:50  16:00 RIMS 204 
Issan Patri (Chennai)
Automorphisms of Compact Quantum Groups
We will study automorphisms of Compact Quantum Groups. We will be define a notion of "inner" automorphism in the grouptheoretic sense and see the behaviour of normal quantum subgroups under these automorphisms. It will turn out that automorphisms are, in a sense, strongly not "inner", give ergodic actions on the the Compact Quantum Group. We will end with a question on finding a suitable automorphism of a Tarski Monster Group, which will show how the quantum case can be very different from the classical one.
Makoto Yamashita (Ochanomizu)
Categorical dual of quantum homogeneous spaces
The notion of compact quantum group actions on operator algebras can be dualized into that of $\mathrm{Rep}(G)$module $\mathrm{C}^*$categories, in the spirit of Woronowicz's TannakaKrein duality. This allows us to give several classification results. First, ergodic actions of $\mathrm{SU}_q(2)$ can be classified in terms of certain weighted graphs, extending the classical McKay correspondence. Second, recasting the noncommutative Poisson boundary in this framework, we obtain an explicit list of the nonKac quantum groups with the same fusion rule and classical dimension of representations as $\mathrm{SU}(n)$. This talk is based on joint works with Kenny De Commer and Sergey Neshveyev.


Dec. 0913 
MATH 110 
Metric geometry and analysis


Dec. 15 Sunday 
10:00  12:00 MATH 110 
Zhizhang Xie (Texas A&M University)
Finitely embeddable groups and strongly finitely embeddable groups
The notion of groups finitely embeddable into Hilbert space was introduced by Weinberger and Yu. It is a more flexible notion than coarse embeddability. For finitely embeddable groups, Weinberger and Yu obtained a lower bound of the freerank of the finite part of Ktheory of the maximal group $\mathrm{C}^*$algebra, which in turn was used to give a lower bound of the size of the structure group of an oriented manifold and to give a lower bound of the size of the space of positive scalar curvature metrics on a given manifold. In order to detect finer information of the structure group and the space of positive scalar curvature metrics, Yu and I were led to the notion of groups with strongly finite embeddability into Hilbert space. It is an open question whether every group is (strongly) finitely embeddable. The talk is based on joint work with Guoliang Yu.


Dec. 1620 
MATH 110 
Further development of AtiyahSinger index theorem and Ktheory


Dec. 2122 
Kinosaki 
Kansai Operator Algebra Seminar


Jan. 07 Tuesday 
16:30  18:00 RIMS 206 
Narutaka Ozawa (RIMS)
A nonseparable amenable operator algebra which is not isomorphic to a $\mathrm{C}^*$algebra
The notion of amenability for Banach algebras was introduced by B. E. Johnson in 1970s and has been studied intensively since then. For several natural classes of Banach algebras, the amenability property is known to single out the “good” members of those classes. For example, B. E. Johnson’s fundamental observation is that the Banach algebra $L_1(G)$ of a locally compact group $G$ is amenable if and only if the group $G$ is amenable. Another example is the celebrated result of Connes and Haagerup which states that a $\mathrm{C}^*$algebra is amenable as a Banach algebra if and only if it is nuclear. In this talk, I will talk about recent progress on the longstanding problem whether every amenable operator algebra is isomorphic to a (necessarily nuclear) $\mathrm{C}^*$algebra. This problem was recently solved in the negative for general nonseparable operator algebras by Choi, Farah and me; and in the affirmative for commutative operator algebras by Marcoux and Popov. The existence of a separable counterexamplethe most interesting caseremains an open problem.


Jan. 14 Tuesday 
16:30  18:00 RIMS 206 
Yasuhiko Sato (Kyoto)
Murrayvon Neumann equivalence for positive elements and order zero c.p. maps
A completely positive map is called order zero if it preserves orthogonality. Recent developments in the classification theorem of $\mathrm{C}^*$algebras suggest that order zero c.p. maps are very compatible with projectionless $\mathrm{C}^*$algebras. In this talk, we investigate the Murrayvon Neumann equivalence for positive elements and see that plays a crucial role for the understanding of order zero c.p. maps and their conjugacy classes. As a consequence of this study, we obtain an affirmative answer to the Toms and Winter conjecture for $\mathrm{C}^*$algebras with a unique tracial state. This talk is based on a joint work with Stuart White and Wilhelm Winter.


Jan. 2931 
RIMS 111 
Development of operator algebras and related topics (program)

