Kyoto Operator Algebra Seminar

April 2017 - August 2017

Apr. 11	15:00 - 16:30 RIMS 206	Yuki Arano (Kyoto) Cohomology of quantum groups Cohomology of a tensor category has been recently introduced by Popa-Shlyakhtenko-Vaes and computed in the quantum sl_2 case by Kyed-Raum-Vaes-Valvekens using the Drinfeld-Yetter resolution obtained by Bichon. In this talk, we compute this cohomology for the higher rank case.
Apr. 14-May 26 TGU Lecture	Sci 3-127	Nigel Higson (Penn State/Kyoto) The Noncommutative Geometry of Tempered Representations April 14(F) 10:00 - 12:00,  21(F) 10:00 - 12:00,  28(F) 10:00 - 12:00 / 14:00-16:00,  May 12(F) 10:00 - 12:00 / 14:00 - 16:00,  19(F) 10:00 - 12:00,  26(F) 10:00 - 12:00.
Apr. 18	15:00 - 16:30 RIMS 206	Yasuyuki Kawahigashi (Tokyo) The relative Drinfeld commutant and alpha-induction We study relative Drinfeld commutants of a fusion category in another fusion category in terms of half-braidings. We identify half-braidings with minimal central projections of the relative tube algebra and certain sectors of the Longo-Rehren subfactors. We apply this general machinery to various fusion categories arising from alpha-induction and compute the relative Drinfeld commutants explicitly.
Apr. 20 Séminaire de travail	10:00 - RIMS 106	Koichi Shimada (Kyoto) Kadison--Singer Problem (Marcus--Spielman--Srivastava Theorem) 1
Apr. 25	15:00 - 16:30 RIMS 206	Narutaka Ozawa (RIMS) Introduction to Tsirelson's Problem Tsirelson's problem (in the weaker form) is one of the most important problem in quantum information theory, which is known to be equivalent to Connes's embedding problem. I will review it from an algorithmic point of view. The lecture also cover Slofstra's recent negative solution to the original (i.e., stronger) Tsirelson problem.
Apr. 26 (Wed) Colloquim	16:30 - 17:30 Sci 3-110	Yusuke Isono (RIMS) フォンノイマン環とdeformation/rigidity理論の紹介
Apr. 27 Séminaire de travail	10:00 - RIMS 106	Koichi Shimada (Kyoto) Kadison--Singer Problem (Marcus--Spielman--Srivastava Theorem) 2
May 09	15:00 - 16:30 RIMS 206	Nigel Higson (PennState/Kyoto) C*-algebras and the uniform admissibility of the discrete series Many aspects of Harish-Chandra’s theory of tempered representations fit very naturally with C*-algebra theory and noncommutative geometry. The principal results are easy to express in the language of C*-algebras, and moreover there are noncommutative-geometric arguments that explain quite conceptually the general form of tempered representation theory, as I shall try to demonstrate. An exception, at least for the time being, is the “uniform admissibility property” of the discrete series. I shall explain what this property is, why it is important, and how it might be approached through C*-algebras and noncommutative geometry.
May 11-13 Workshop	Sci 3-127	Advances in non commutative geometry
May 16	15:00 - 16:30 RIMS 206	Yasuhiko Sato (Kyoto) Actions of amenable groups and absorption of the Jiang-Su algebra In the recent classification theory of $\mathrm{C}^*$-algebras, the absorption of the Jiang-Su algebra $\mathcal{Z}$ plays a central role. Actually, A. S. Toms and W. Winter conjectured that $\mathcal{Z}$-absorption is equivalent to other regularity properties, such as strict comparison and finiteness of nuclear dimension, for standard nuclear $\mathrm{C}^*$-algebras. Now, we know that this conjecture holds true under the assumption of unique tracial state. In this talk, we study a permanence property of $\mathcal{Z}$-absorption for crossed products by countable amenable groups. Assuming strict comparison and uniqueness of tracial state, we show that the crossed product of unital separable simple nuclear $\mathrm{C}^*$-algebra absorbs the Jiang-Su algebra again.
May 23	15:00 - 16:30 RIMS 206	Norio Nawata (Osaka Kyoiku) Trace scaling automorphisms of $\mathcal{W}\otimes\mathbb{K}$ We classify trace scaling automorphisms of $\mathcal{W}\otimes\mathbb{K}$ up to outer conjugacy, where $\mathcal{W}$ is a certain simple separable nuclear stably projectionless C$^*$-algebra having trivial $K$-groups. Mainly, we talk about a homotopy type theorem of unitaries in the central sequence C$^*$-algebra $F(\mathcal{W})$ of $\mathcal{W}$.
May 25	10:45 - 11:45 Sci 3-108	Tulio Gaxiola (CIMAT&Tohoku) Spectral Analysis of Graphs: a Non-Commutative Probabilistic outlook In this talk we introduce some results about the relation of spectral distributions of some products of graphs with notions of non-commutative independece. Moreover, we explain recent results, in collaboration with Octavio Arizmendi, on spectral distribution of distance-k graphs of star and free products of graphs.
May 25	13:15 - 14:15 Sci 3-108	Camille Male (Bordeaux & CNRS) Non commutative notions of independences The convergence in traffic distribution of matrices enriches the convergence in non commutative distribution, and makes tractable the description of the limiting distribution of matrices invariant in law by permutation of the elements of the basis (in particular, of random graphs). In this presentation I will present three particular situations where the traffic independence reduces respectively to the free, the tensor or the Boolean independence.
May 29-02 Intensive Lecture Course	Sci 3-127	Yoshimichi Ueda (Kyushu) ランダム行列に対する大偏差原理 29(M) 15:00 - 17:00,  30(T) 15:00 - 17:00,  31(W) 10:00 - 12:00,  01(T) 15:00 - 17:00,  02(F) 10:00 - 12:00. Colloquium May 31(W), 16:30 - 17:30 ランダム行列の固有値経験分布に対する大偏差原理を解説する．また，ランダム行列（の固有値経験分布）の行列サイズ無限大極限を記述する自然な枠組みとしての自由確率論を紹介する．なお，学部で習う標準的な測度論の知識は仮定するが，確率論の特別な知識は仮定しない．
May 31 (Wed) Colloquim	16:30 - 17:30 Sci 3-110	Yoshimichi Ueda (Kyushu) ランダム行列と作用素環
June 01 Séminaire de travail	10:00 - RIMS 106	Koichi Shimada (Kyoto) Kadison--Singer Problem (Marcus--Spielman--Srivastava Theorem) 3
June 15 Séminaire de travail	10:00 - RIMS 106	Koichi Shimada (Kyoto) Kadison--Singer Problem (Marcus--Spielman--Srivastava Theorem) 4
June 20	15:00 - 16:30 RIMS 206	Reiji Tomatsu (Hokkaido) Ultraproducts of crossed product von Neumann algebras I will explain how to treat an ultraproduct von Neumann algebra of a crossed product von Neumann algebra using the notion of equicontinuity.
June 26-28 Workshop	RIMS 110	Mathematical Aspects of Quantum Fields and Related Topics
July 05 (Wed) Colloquim	16:30 - 17:30 RIMS 110	Yuki Arano (Kyoto) 部分因子環論と表現論
July 11	15:00 - 16:30 RIMS 206	Sakie Suzuki (RIMS) The universal quantum invariant and colored ideal triangulations The Drinfeld double of a finite dimensional Hopf algebra is a quasi-triangular Hopf algebra with the canonical element as the universal R-matrix, and one can obtain a ribbon Hopf algebra by adding the ribbon element. The universal quantum invariant of framed links is constructed using a ribbon Hopf algebra. In that construction, a copy of the universal R-matrix is attached to each crossing, and invariance under the Reidemeister III move is shown by the quantum Yang-Baxter equation of the universal R-matrix. On the other hand, the Heisenberg double of a finite dimensional Hopf algebra has the canonical element (the S-tensor) satisfying the pentagon relation. In this talk we reconstruct the universal quantum invariant using the Heisenberg double, and extend it to an invariant of equivalence classes of colored ideal triangulations of 3-manifolds up to colored moves. In this construction, a copy of the S-tensor is attached to each tetrahedron, and invariance under the colored Pachner (2,3) moves is shown by the pentagon relation of the S-tensor. 任意の有限次元ホップ代数のDrinfeld doubleはcanonical elementを普遍R行列にもつquasi-triangularホップ代数になり．さらにリボン元を付け加えることでリボンホップ代数が得られる．普遍量子不変量とはリボンホップ代数と絡み目図式を用いて構成される枠付き絡み目の不変量である．その構成の中では図式の正交点に普遍R行列が対応し，普遍R行列の量子Yang-Baxter方程式がライデマイスターIII移動の下での不変性を保証する．一方，任意の有限次元ホップ代数のHeisenberg doubleのcanonical element（Sテンソル）は5角関係式を満たす．この講演ではHeisenberg doubleを用いて普遍量子不変量を絡み目補空間の色付き理想単体分割の不変量として再構成し，さらにそれを絡み目補空間の色付き理想単体分割の不変量として拡張する．この構成では理想単体にSテンソルが対応し，色付き理想単体分割のPachner (2,3) moveの下での不変性をSテンソルの５角関係式が保証する．
July 13 Séminaire de travail	10:00 - RIMS 106	Narutaka Ozawa (RIMS) Strong property (T) after Lafforgue
July 18 Hakubi Seminar	16:30 - Hakubi Center	Yusuke Isono (RIMS) フォンノイマン環論の紹介 フォンノイマン環論とは，フォンノイマンが量子力学を研究するために作った数学理論である． 非常に雑に言えば，大学一年生で学ぶ線形代数を「無限に大きなサイズの行列」に対して考えるものである． 当初は物理学への応用を念頭において研究されていたが，現在では純粋な数学理論としても研究されている． 実際，K理論，結び目，エルゴード理論，表現論など多くの数学理論と密接に関係しており，非常に興味深い数学理論である． 一方で，無限次元である事が原因で，その取扱いは極めて難解である． いわゆる代数，幾何，解析のそれぞれの知識を活用した研究が必要とされる．この講演では，数学理論としてのフォンノイマン環論の紹介を行う．特に予備知識は仮定せず， どのように定義されるのか，どのような点が難しいのか，どのような問題を考えているのか， 等の基本的な事を理解してもらう事を目標とする．
July 20 Séminaire de travail	10:00 - RIMS 106	Yuki Arano (Kyoto) Classification of subfactors of finite depth (after Popa)
July 25 Séminaire de travail	15:00 - RIMS 206	Hiroshi Ando (Chiba) Noncommutative Grothendieck inequality and amenability of nuclear C* algebras (after Haagerup)
July 26 Wed	Sci 3-127	Workshop on interactions between commutative and noncommutative probability
Sep. 04-06	RIMS 111	Recent developments in operator algebras (program)
Oct. 05 DT seminar	15:00 - 16:30 Sci 6-609	Raphael Ponge (Seoul) Cyclic homology and group actions on manifolds
Oct. 11 Colloquim	16:30 - 17:30 RIMS 110	Mikael Pichot (McGill/RIMS) Nonpositive curvature and operator algebras The field of operator algebras was begun in the late 1920's by J. von Neumann, through his work on abstract Hilbert spaces and the foundation of quantum mechanics. The subject developed steadily for nearly a century, and found deep connections with many branches of mathematics. The talk will discuss, using concrete examples, some of these connections, in particular with group theory and geometry of nonpositive curvature. The main focus will be the recent work of Sylvain Barré and myself on intermediate rank geometry. I will give some motivation for this work, and explain some of the leading ideas in the study of discrete groups of intermediate rank.
Oct. 17	15:00 - 16:30 RIMS 206	Masaki Izumi (Kyoto) Group Actions on Kirchberg Algebras
Oct. 31 DT Seminar	15:00 - 16:30 Sci 6-609	François Dahmani (Grenoble) Conjugacy of automorphisms: on the conjugacy problem for certain automorphisms of free groups
Nov. 01 Séminaire de travail	13:30 - RIMS 109	Yuki Arano (Kyoto) Maharam
Nov. 07 DT Seminar	15:00 - 16:30 Sci 6-609	Tomohiro Fukaya (TMU) Coarse Cartan-Hadamard theorem and an application to the coarse Baum-Connes conjecture
Nov. 14	15:00 - 16:30 RIMS 206	Yoshikata Kida (Tokyo) Central sequences in the full group and compact extensions We discuss when an orbit equivalence relation admis a non-trivial central sequence in its full group. Among others, we show that existence of such a sequence is stable under compact extension of equivalence relations. Related results and examples are also discussed.
Nov. 15 Séminaire de travail	13:30 - RIMS 109	Takuya Takeishi (RIMS) Semigroup actions and K-theory (after arxiv:1205.5412)
Nov. 17-19	Ritsumei BKC	Annual Meeting on operator theory & operator algebra theory
Nov. 21	15:00 - 16:30 RIMS 206	Kei Hasegawa (Kyushu) Boundary rigidity for free product C*-algebras For a reduced free product of C*-algebras, we prove a boundary rigidity result for the embedding of it into the associated ``crossed product'' C*-algebra under the assumption that the GNS representations associated with the distinguished states are essential and one of free components satisfies a suitable diffuseness condition. This provides new examples of rigid embeddings of exact C*-algebras into purely infinite simple nuclear C*-algebras.
Nov. 22 Séminaire de travail	13:30 - RIMS 109	Yusuke Isono (RIMS) Locally compact group actions and Cartan rigidity (after arxiv:1703.09092)
Nov. 28	15:00 - 16:30 RIMS 206	Narutaka Ozawa (RIMS) Kazhdan's property (T) and semidefinite programming Kazhdan's property (T) for groups has a number of applications in pure and applied mathematics. It has long been thought that groups with property (T) are rare among the "naturally-occurring" groups, but it may not be so and it may be possible to observe this by extensive computer calculations. After an introduction, I will present a computer assisted (but mathematically rigorous) method of confirming property (T) based on semidefinite programming with some operator algebraic input. I will report the progress recently made in collaboration with M. Kaluba, P. Nowak, and PL-grid, a Polish supercomputer. It confirms property (T) of Aut(F_5), which solves a well-known problem in geometric group theory, at least partially, leaving the tantalizing question in the case of Aut(F_d), d=4 and d>5, unsettled.
Dec. 01 DS Seminar	14:00 - 17:00 Sci 6-609	Masaki Tsukamoto (Kyoto) Expansive multiparameter actions and mean dimension
Dec. 05	15:00 - 16:30 RIMS 206	Mikael Pichot (McGill/RIMS) On Aut(F_2) I will explain things related to the automorphism group of $F_2$ from a geometric perspective.
Dec. 09	OKU Tennōji	Kansai Seminar
Dec. 11 VOA workshop	10:00 - 10:50 RIMS 420	Yasuyuki Kawahigashi (Tokyo) Representation theories of vertex operator algebras and operator algebras
Dec. 19	15:00 - 16:30 RIMS 206	Makoto Yamashita (Ochanomizu) Tube representations of graded categories We study the structure of tube algebra under graded twist of tensor categories. This deformation scheme played a central role in the Kazhdan-Wenzl classification of semisimple tensor categories with the fusion rules of $\mathrm{SL}_n$, and at the simplest case it relates quantum $\mathrm{SU}(2)$ group at the parameter $q$ and $-q$. Motivated by the 2-cocycle deformation result for tube algebras of pointed categories due to Bisch, Das, Ghosh, Rakshit, we give a general formula describing annular algebra of 3-cocycle deformation categories as 2-cocycle deformation of Fell bundle over a groupoid. Based on joint work with Bhowmick, Ghosh, Rakshit.
Dec. 20 Séminaire de travail	13:30 - RIMS 109	Yuki Arano (Kyoto) Subfactor
Jan. 09	15:00 - 16:30 RIMS 206	Jean Roydor (Bordeaux/Jussieu) Banach-Mazur stability of von Neumann algebras We study perturbation of von Neumann algebras relatively to the Banach-Mazur distance. We prove that, under some cohomological conditions, two von Neumann algebras which are close are necessarily Jordan isomorphic (thus isometric).
Jan. 23	15:00 - 16:30 RIMS 206	Ulrich Pennig (Cardiff) A Dixmier-Douady theory for strongly self-absorbing C*-algebras I will report on joint work with Marius Dadarlat. We showed that the Dixmier-Douady theory of continuous fields of C*-algebras with compact operators as fibres extends to a more general theory of fields with fibres stabilised strongly self-absorbing C*-algebras. The classification of the corresponding locally trivial fields involves a generalised cohomology theory obtained from the unit spectrum of topological K-Theory, which is computable via the Atiyah-Hirzebruch spectral sequence. An important feature is the appearance of characteristic classes in higher dimensions. We found a necessary and sufficient K-theoretical condition for local triviality of these continuous fields over spaces of finite covering dimension.
Jan. 24-26	RIMS 420	Mathematical study on topological phases (program)
Feb. 07 Wednesday	13:00 - 14:30 Sci 3-109	Hao-Wei Huang (Sun Yat-sen Univ) Bi-freely infinite divisibility of unitary faces In free probability theory the notion of free multiplicative convolution of probability distributions on the unit circle has played an important role since its inception by Voiculescu some $30$ years ago. In 2013, Voiculescu generalized the notion of free independence to study left and right actions on reduced free product spaces simultaneously, known as bi-free independence. One generalization of the free multiplicative convolution to the bi-free setting is the bi-free multiplicative convolution of probability distributions on the unit bi-torus. In this talk, we will introduce an analytic machinery to study Voiculescu's bi-free partial $S$-transform and use it to characterize the multiplicative bi-free infinite divisibility on the unit bi-torus. This is joint work with J.-C. Wang.
Feb. 16 Friday	14:30 - 16:00 Sci 3-109	Sven Raum (EPFL) Cartan subalgebras in dimension drop algebras I will report about recent work on Cartan subalgebras of stabilised dimension drop algebras. Starting with an introduction to the topic, which includes motivation, I will proceed to explain a complete classification up to conjugacy by an automorphism of Cartan subalgebras in dimension drop algebras with coprime parameters. Moreover, in this setting two Cartan subalgebras are conjugate if and only if their spectrum is homeomorphic, providing the tamest possible classification result for C*-algebraic Cartan subalgebras. This is joint work with S. Barlak.
	16:15 - 17:45 Sci 3-109	Xin Li (QMUL) Constructing Cartan subalgebras in classifiable C*-algebras After brief introductions to Elliott's classification programme and Cartan subalgebras in C*-algebras, I will explain how to construct Cartan subalgebras in large classes of classifiable C*-algebras.
Feb. 20	14:30 - 16:00 RIMS 206	Michiya Mori (Tokyo) Tingley's problem for operator algebras Tingley's problem asks whether every surjective isometry between the unit spheres of two Banach spaces admits an extension to a real linear surjective isometry between the whole spaces. Tingley's problem between real Banach spaces has been considered for more than 30 years. In recent years, using the facial structure of unit balls, some researchers solved Tingley's problem between operator algebras affirmatively in several settings. In this talk, I explain the history of this problem and my new results concerning Tingley's problem for operator algebras.
	16:15 - 17:45 RIMS 206	Alessandro Carderi (Dresden) Asymptotic invariants of lattices in locally compact groups The aim of our work is to understand some of the asymptotic properties of sequences of lattices in a fixed locally compact group. As an example we are interested in the asymptotic growth of the Betti numbers of the lattices renormalized by the covolume or the rank-gradient, the minimal number of generator also renormalized by the covolume. For doing so we will consider the ultraproduct of the actions of the locally compact group on the coset spaces and we will show how the properties of one of its cross sections are related to the asymptotic properties of the lattices.