Mar. 28  Apr. 04 
RIMS 420 
KTGUIMU Mathematics Colloquia and Seminars


May 17 
14:00  15:30 RIMS 206 
Hiroshi Ando (Chiba)
Unitarizability, MaureyNikishin factorization and Polish groups of finite type
In the seminal work of cocylcle superrigidity theorem, Sorin Popa introduced the class of finite type Polish groups. A Polish group $G$ is of finite type, if it is embeddable into the unitary group of a separable II$_1$ factor equipped with the strong operator topology. Popa proposed a problem of finding abstract characterization of finite type Polish groups. As Popa pointed out, there are two conditions which are clearly necessary for a Polish group $G$ to be of finite type, namely that
(a) $G$ is unitarily representable (i.e., $G$ is embeddable into the full unitary group of $\ell^2$)
and
(b) $G$ is SIN, i.e., $G$ admits a twosided invariant metric compatible with the topology.
Popa asked whether these two conditions are actually sufficient. In 2011, Yasumichi Matsuzawa and I obtained several partial positive answers for some classes of Polish groups. In this talk, we show that there exists a unitarily representable SIN Polish group which is not of finite type, answering the above question. Our analysis is based on the MaureyNikishin Theorem on bounded maps from a Banach space of Rademacher type 2 to the space of all measurable
maps on a probability space.
This is joint work with Yasumichi Matsuzawa, Andreas Thom, and Asger Törnquist.


May 30  June 03 
RIMS 420 
Geometric Analysis on Discrete Groups


June 07 
14:00  15:30 RIMS 206 
Yusuke Isono (RIMS)
Biexact groups, strongly ergodic actions and group measure space type III factors with no central sequence
We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras arising from arbitrary actions of biexact discrete groups (e.g. free groups) on amenable von Neumann algebras. We particularly prove a spectral gap rigidity result for the crossed products and, using recent results of BoutonnetIoanaSalehi Golsefidy, we provide examples of group measure space type III factors with no central sequences. This is joint work with C. Houdayer.


July 06&08 
11:00  12:30 Sci 3305 
Saeid Molladavoudi (uOttawa)
Symmetry Reduction in Quantum Information Theory
Symmetries are ubiquitous in natural phenomena and so in their mathematical descriptions and according to a general principle in Mathematics, one should exploit a symmetry to simplify a problem whenever possible. In these minilecture series, we focus on elimination of symmetries from multiparticle quantum systems and discuss that the existing methods equip us with a powerful set of tools to compute geometrical and topological invariants of the resulting reduced spaces.
We first introduce some of the grouptheoretical and geometrical settings that are required to study multiparticle quantum systems and present a mathematical framework for symmetry reduction purposes, namely characterizing the space of entanglement classes of multiparticle quantum states provided the local information encoded in their local density matrices.
Then, as an intermediate step, we consider the maximal torus subgroup $T$ of the compact Lie group of Local Unitary operations $K$ and elaborate on the symmetry reduction procedure and use methods from symplectic geometry and algebraic topology to obtain some of the topological invariants of these relatively wellbehaved quotients for multiparticle systems containing $r$ qubits. More precisely, by fixing the relative phases of isolated $r$ qubits and then varying them inside their domain in an $r$dimensional polytope, we utilize recursive wallcrossing procedures to obtain some of the topological invariants of the corresponding reduced spaces, e.g. Poincaré polynomials and Euler characteristics.


July 10 
Kyoto 
Kyoto Prize Symposium (For a general audience. Registration required.)


July 12 
13:30  15:00 RIMS 206 
Richard Cleve (Waterloo)
Entangled strategies for linear system games
Binary linear system games provide a simple framework for investigating the nonlocal effects that can occur from entangled quantum states. In particular, perfect strategies for such games are characterized by operator solutions to certain noncommutative equations: finitedimensional solutions for tensorproduct entanglement; and possiblyinfinitedimensional solutions for commutingoperator entanglement. I will explain some context and motivation for considering these games and then prove the characterizations. The proofs are based around a finitelypresented group associated with the linear system. This is joint work with Rajat Mittal, Li Liu and William Slofstra.


July 12 
15:15  16:45 RIMS 206 
Henry Tucker (USC)
FrobeniusSchur indicators and modular data for singlygenerated fusion categories
FrobeniusSchur indicators provide an important invariant for fusion categories, especially for application to classification problems. Their values can be obtained from the modular data of the Drinfel'd center. In several important cases of singlygenerates fusion categories this modular data is given by quadratic forms on some associated groups. This leads to the expression of the indicators as quadratic Gauss sums, which yields examples of fusion categories that are completely determined by their indicators. We will discuss the indicators of neargroups and HaagerupIzumi categories following from the conjectures of Evans and Gannon regarding the modular data for the centers of these categories.


July 19 
14:00  15:30 RIMS 206 
Takuya Takeishi (Kyoto)
Primitive ideals and Ktheoretic approach to BostConnes systems
We would like to deal with the classification problem of BostConnes systems. For a number field $K$, there is a $\mathrm{C}^*$dynamical system ($\mathrm{C}^*$algebra equipped with an $\mathbf{R}$action) so called the BostConnes system for $K$. By KMSclassification theorem of LacaLarsenNeshveyev, the Dedekind zeta function is an invariant of BostConnes systems. However, this invariant turned out to be an invariant of BostConnes $\mathrm{C}^*$algebras (without $\mathbf{R}$acitons),. In this talk, we will introduce definitions and some basic facts about BostConnes systems, and give an outline of the proof of this theorem.


Aug. 0112 
Sendai 
MSJSI: Operator Algebras and Mathematical Physics


September 0509 KTGU Lecture 
Sci 3127 
Sorin Popa (UCLA/Kyoto)
Paving over arbitrary MASAs in von Neumann algebras
05(M) 15:00  17:00, 06(T) 15:00  17:00, 07(W) 15:00  17:00, 08(T) 15:00  17:00, 09(F) 15:00  17:00.
Motivated by an intriguing claim in Dirac's 1947 book on "Quantum Mechanics", Kadison and Singer have asked the question of whether any pure state on the diagonal maximal abelian subalgebra (MASA) $D$ of $B(H)$ extends to a unique state on $B(H)$. They also showed that this unique pure state extension property is equivalent to norm paving over $D$ for operators in $B(H)$. The KadisonSinger paving problem has been recently solved in the affirmative by MarcusSpielmanSrivastava. In these lectures, we will introduce a general paving property for a MASA $A$ in a von Neumann factor $M$, called sopaving, involving approximation in the sotopology, rather than in norm, but which coincides with normpaving in the case $D\subset B(H)$. We conjecture that sopaving holds true for any MASA in any factor. We check the conjecture in many cases, including singular and regular MASAs in hyperfine factors. Related problems will be discussed.


Sep. 1214 
RIMS 420 
Recent developments in operator algebras
(program)


Oct. 0911 
Maebashi 
Annual meeting on operator theory & operator algebra theory


Oct 18 
15:00  16:30 RIMS 206 
Yusuke Isono (RIMS)
Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors
Let $M$ be a type $\mathrm{III}$ factor associated with a free (unitary or orthogonal) quantum group. We prove that for any factor $B$, the tensor product of $M$ and $B$ has no Cartan subalgebras. The main ingredient of the proof is a generalization of OzawaPopa and PopaVaes's weakly compact action at the level of the continuous core. We study it by using an operator valued weight to $B$ and the central weak amenability of $M$.


Oct 25 
15:00  16:30 RIMS 206 
Koichi Shimada (Kyoto)
Maximal amenability of the generator subalgebra in qGaussian von Neumann algebras
We give explicit examples of maximal amenable von Neumann subalgebras of the $q$Gaussian von Neumann algebras. More precisely, the generator subalgebra is maximal amenable inside the $q$Gaussian algebras for real numbers $q$ with $q<1/9$. We would like to show this based on Popa's theory. In order to achieve this, we construct a Riesz basis in the spirit of Radulescu. This is a joint work with Sandeepan Parekh and Chenxu Wen.


Nov 01 
15:00  16:30 RIMS 206 
Ivan Ip (Kyoto)
Positive representations: a bridge between DrinfeldJimbo quantum groups and C*algebra
The finite dimensional representation theory of DrinfeldJimbo quantum group is wellknown for representation theorist, and many applications have been discovered in the last 30 years. However, the noncompact case is a lot more complicated and much less is known. The notion of "positive representations" was introduced in a joint work with I. Frenkel to study the representation theory of split real quantum groups, which involves representations by unbounded operators. In this talk, I will give some motivations for such representation theory, and explain how the techniques from C*algebra allow us to study the harmonic analysis and braiding structure of split real quantum groups.


Nov 11 RT Seminar 
16:30  18:00 RIMS 402 
Benoit Collins (Kyoto)
Positivity for the dual of the TemperleyLieb basis
A problem raised by Vaughan Jones is to consider the basis dual to the canonical basis of the TemperleyLieb algebra for nondegenerate loop values, and investigate the coefficients of this basis element in the original basis. For example, the dual of the identity element is a multiple of the Jones Wenzl projection, and computing it is an important problem for which some formulas have been given recently (e.g. by Morrisson). The goal of this talk is to describe a new combinatorial formula for all of these coefficients. As a byproduct, we solve one question of Jones and prove that all these coefficients are never zero for real parameters $\ge 2$, and we compute their sign. Our strategy relies on identifying these coefficients with the Weingarten function of the free orthogonal quantum group, and on developing quantum integration techniques. I will spend some time on recalling definitions and properties of some objects that are less wellknown, such as Weingarten functions and free orthogonal quantum groups. This talk is based on joint work with Mike Brannan, arXiv:1608.03885.


Nov 29 
15:00  16:30 RIMS 206 
Yuki Arano (Tokyo)
Torsionfreeness for fusion rings and tensor C*categories
Torsionfreeness for discrete quantum groups was introduced by R. Meyer in order to formulate a version of the BaumConnes conjecture for discrete quantum groups. In this talk, we define torsionfreeness for abstract rigid tensor C*categories and abstract fusion rings and show that the free unitary quantum group is torsionfree. This is joint work with Kenny De Commer.


Dec 06 
15:00  16:30 RIMS 206 
Zhigang Bao (Hong Kong)
Local law of addition of random matrices
The question of how to describe the possible eigenvalues of the sum of two general Hermitian matrices dates back to Weyl. A randomized version of this question can give us a "deterministic" answer. Specifically, when two largedimensional matrices are in general position in the sense that one of them is conjugated by a random Haar unitary matrix, the eigenvalue distribution of their sum is asymptotically given by the free convolution of the respective eigenvalue distributions. This result was obtained by Voiculescu on the macroscopic scale. In this talk, we show that this law also holds in a microscopic scale. This allows us to get an optional convergence rate for Voiculescu's result.


Dec. 10 Sat 
OsakaKyoiku U 
Kansai Operator Algebra Seminar


Dec 13 
15:00  16:30 RIMS 206 
Raphael Ponge (Seoul)
The Cyclic Homology of CrossedProduct Algebras
This talk will be a preliminary report on an explicit computation of the cyclic homology and periodic cyclic homology of crossedproduct algebras over commutative rings. By explicit computation it is meant the construction of explicit quasiisomorphisms. This enables us to recover and somewhat simplify various known results by BaumConnes, BrylinskiNistor, Crainic, FeiginTsygan, GetzlerJones, Nistor, among others. In particular, we recover the spectral sequences of FeiginTsygan and GetzlerJones, and obtain several other spectral sequences as well. The approach is purely algebraic. It grew out of an attempt to extend to crossedproduct algebras the algebraic approach of Marciniak to the computation of the cyclic homology of group rings by Burghelea. At the conceptual level, we introduce a generalization of the cyclindrical complexes of GetzlerJones. This provides us with the rele vant homological tool to understand the cyclic homology of crossedproduct algebras, especially in the nontorsion case. The results extend to the cyclic homology of crossedproducts associated with locally convex algebras. In particular, in the case of group actions on manifolds we obtain an explicit construction of cyclic cycles in terms of equivariant characteristic classes.


Dec 20 
14:30  16:00 RIMS 206 
Yosuke Kubota (Tokyo)
Compact Lie group actions on C*algebras with the continuous Rokhlin property
The Rokhlin property is a dynamical analogue of freeness of group actions on C*algebras. In this talk, we deal with its variation, the continuous Rokhlin property, which is compatible with KKtheory. We give a complete classification of equivariant Kirchberg algebras with the continuous Rokhlin property when G is a compact Lie group with torsionfree fundamental group. For the proof, the BaumConnes isomorphism for the Pontrjagin dual quantum group plays an essential role. This is joint work with Yuki Arano.


Jan 10 
14:00  15:00 RIMS 206 
Takuya Kawabe (RIMS)
On the ideal structure of reduced crossed products
Let $X$ be a compact Hausdorff space with an action of a countable discrete group $\Gamma$. We say that $X$ has the intersection property if every nonzero ideals in its reduced crossed product has a nonzero intersection with $C(X)$. We characterize the intersection property of $X$ by a certain property for amenable subgroups of its stabilizer subgroups in terms of the Chabouty space of $\Gamma$. This generalizes Kennedy's algebraic characterization of the simplicity for a reduced group $\mathrm{C}^{*}$algebra of a countable discrete group.


Jan 10 
15:30  16:30 RIMS 206 
Yul Otani (Tokyo)
Entanglement entropy in algebraic quantum field theory
We consider the problem of defining the entanglement entropy for chiral nets in the framework of algebraic quantum field theory. Considering a Möbius covariant local net with the split property, we give a sensible definition for the entropy of a state restricted to a local algebra of an open connected nondense interval $I$, with a given conformal energy cutoff $E$. Considering the vacuum state restricted to any such interval, we prove that the latter is finite, and we give some upper bound estimates in terms of the dimensions of eigenspaces of the conformal Hamiltonian. This talk is based on a joint work with Yoh Tanimoto.


Jan 24 
15:00  16:30 RIMS 206 
Kei Hasegawa (Kyushu)
BassSerre trees of amalgamated free product C*algebras
For a given reduced amalgamated free product of C$^*$algebras, we introduce a C$^*$algebra including it as a unital subalgebra. This C$^*$algebra is an analogue of the crossed product of the compactification of the BassSerre tree associated with an amalgamated free product group, and naturally identified with a CuntzPimsner algebra. As applications we give simple proofs of several known results about exactness, nuclearity and KKtheory for reduced amalgamated free products.


Feb. 0103 
RIMS 111 
Operator Algebras and Quantum Information Theory
(program)


Feb 09 Thursday 
15:00  16:30 RIMS 110 
Amine Marrakchi (ParisSud)
Spectral gap for full type III factors
We present new spectral gap characterizations for full type III factors, generalizing a theorem of Connes in the tracial case, and we give applications to the fullness of tensor products factors and crossed product factors. We will also discuss some related open problems. This is partly joint work with Cyril Houdayer and Peter Verraedt.


Mar 08 Wednesday 
15:00  16:30 Sci 3305 
Takeshi Katsura (Keio)
On magic square C*algebras
In '98, Wang defined a series of quantum groups $A_s(n)$ ($n=1, 2, \ldots$) which are free versions of the symmetric groups $\mathfrak{S}_n$. Wang remarked that for $n=1, 2, 3$, $A_s(n)$ becomes the classical one, i.e. $C(\mathfrak{S}_n)$, and that for $n \geq 4$, $A_s(n)$ is noncommutative. In '08, Banica and Collins showed that $A_s(4)$ can be embedded into the homogeneous C*algebra $C(SU_2, M_4(\mathbb{C}))$ by using integration techniques.
In this talk, we focus on the underlying C*algebras of the quantum groups $A_s(n)$ which we call the magic square C*algebras. After general discussion on the magic square C*algebras $A_s(n)$, we give another proof of the embedding of $A_s(4)$ into $C(SU_2,M_4(\mathbb{C}))$ using crossed products. As a byproduct of our proof, we give an explicit computation of the image of the embedding. The talk is based on the master thesis of my student Masahito Ogawa.

