# 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) tHmC}deformation/rigidity_̏Љ 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-Chandrafs 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 guniform admissibility propertyh 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) _sɑ΂΍ 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 _šŗLlozɑ΂΍D܂C_sǐŗLlozj̍sTCYɌLq鎩RȘgg݂ƂĂ̎Rm_ЉDȂCwŏKWIȑx_̒m͉肷邪Cm_̓ʂȒm͉肵ȂD May 31 (Wed) Colloquim 16:30 - 17:30 Sci 3-110 Yoshimichi Ueda (Kyushu) _sƍpf 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) q_ƕ\_ 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. Cӂ̗Lzbv㐔Drinfeld doublecanonical element𕁕Rsɂquasi-triangularzbv㐔ɂȂDɃ{t邱ƂŃ{zbv㐔D՗ʎqsϗʂƂ̓{zbv㐔Ɨݖڐ}pč\gtݖڂ̕sϗʂłD̍\̒ł͐}̐_ɕRs񂪑ΉCRs̗ʎqYang-BaxterCf}CX^[IIIړ̉ł̕sϐۏ؂DCCӂ̗Lzbv㐔Heisenberg doublecanonical elementiSe\j5p֌W𖞂D̍ułHeisenberg doublepĕ՗ʎqsϗʂ𗍂ݖڕԂ̐FtzP̕̕sϗʂƂčč\Cɂ𗍂ݖڕԂ̐FtzP̕̕sϗʂƂĊgD̍\ł͗zP̂Se\ΉCFtzP̕Pachner (2,3) movẻł̕sϐSe\̂Tp֌Wۏ؂D 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) tHmC}_̏Љ tHmC}_Ƃ́CtHmC}ʎq͊w邽߂ɍw_łD ɎGɌ΁CwNŊwԐ㐔uɑ傫ȃTCY̍svɑ΂čl̂łD ͕wւ̉pOɂČĂC݂ł͏Ȑw_ƂĂĂD ہCK_CіځCGS[h_C\_ȂǑ̐w_ƖڂɊ֌WĂCɋ[w_łD ŁCł鎖ŁC̎戵͋ɂ߂ēłD 㐔C􉽁C͂̂ꂼ̒mpKvƂD̍uł́Cw_ƂẴtHmC}_̏ЉsDɗ\m͉肹C ǂ̂悤ɒ̂Cǂ̂悤ȓ_̂Cǂ̂悤ȖlĂ̂C ̊{IȎ𗝉Ă炤ڕWƂD 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

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