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 29 
15:00  16:30 RIMS 206 
Yuki Arano (Tokyo)
TBA
tba


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 13 
15:00  16:30 RIMS 206 
Raphael Ponge (Seoul)
TBA
tba


Dec 20 
15:00  16:30 RIMS 206 
TBA (***)
TBA
tba

