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)

