Apr. 04 
15:00  18:00 RIMS 209 
Roadmap Meeting


Apr. 07 
14:00  15:30 RIMS 206 
Yuhei Suzuki (Tokyo)
Construction of minimal skew products of amenable minimal dynamical systems
We give a generalization of a result of Glasner and Weiss. This provides many new examples of amenable minimal dynamical systems of
exact groups. We also study the pure infiniteness of the crossed products of minimal dynamical systems arising from this result. For this purpose, we introduce and study a notion of the finite filling property for etale groupoids, which generalizes a result of Jolissaint and Robertson. As an application, we show that for any connected closed topological manifold M, every countable nonamenable exact group admits an amenable minimal free dynamical system on the product of M and the Cantor set whose crossed product is a Kirchberg algebra. This extends a result of Rørdam and Sierakowski.


Apr. 14 DT Seminar 
15:00  16:30 Sci 6609 
Masato Mimura (Tohoku)
New algebraization of Kazhdan and fixed point properties


Apr. 14 
16:45  18:15 RIMS 206 
SeungHyeok Kye (Seoul)
Various notions of positivity for bilinear maps and applications to tripartite entanglement
We consider bilinear analogues of $s$positivity for linear maps. The dual objects of these notions can be described in terms of Schimdt ranks for tritensor products and Schmidt numbers for tripartite quantum states. These tripartite versions of Schmidt numbers cover various kinds of biseparability, and so we may interpret witnesses for those in terms of bilinear maps. We give concrete examples of witnesses for various kinds of three qubit entanglement. This is a cowork with Kyung Hoon Han.


May 12 
15:00  16:30 RIMS 206 
Igor Klep (Auckland)
Commuting Dilations and Linear Positivstellensätze
Given a tuple $A=(A_1,...,A_g)$ of real symmetric matrices of the same size, the affine linear matrix polynomial $L(x):=I\sum A_j x_j$ is a monic linear pencil. The solution set $S_L$ of the corresponding linear matrix inequality, consisting of those $x$ in ${\mathbb R}^g$ for which $L(x)$ is positive semidefinite (PsD), is called a spectrahedron. It is a convex semialgebraic subset of ${\mathbb R}^g$. We study the question whether inclusion holds between two spectrahedra. We identify a tractable relaxation of this problem by considering the inclusion problem for the corresponding free spectrahedra $D_L$. Here $D_L$ is the set of tuples $X=(X_1,...,X_g)$ of symmetric matrices (of the same size) for which $L(X):=I\sum A_j \otimes X_j$ is PsD.
We explain that any tuple $X$ of symmetric matrices in a bounded free spectrahedron $D_L$ dilates, up to a scale factor, to a tuple $T$ of commuting selfadjoint operators with joint spectrum in the corresponding spectrahedron $S_L$. The scale factor measures the extent that a positive map can fail to be completely positive. In the case when $S_L$ is the hypercube $[1,1]^g$, we derive an analytical formula for this scale factor, which as a byproduct gives new probabilistic results for the binomial and beta distributions.
The talk is based on joint work with Bill Helton, Scott McCullough and Markus Schweighofer.


May 26 
10:30  12:00 Sci 3152 
Nigel Higson (Penn State University)
The Oka principle: commutative and noncommutative
Kiyoshi Oka proved in 1938 that topological line bundles over closed, complex submanifolds of complex affine space admit unique holomorphic structures. Nearly twenty years later, Hans Grauert proved the same theorem for topological vector bundles of any rank. I will examine these results from the point of view of Ktheory, and explain the proofs, which are strikingly similar to the proofs of some fundamental theorems in homology theory, for example the Jordan separation theorem. Oka’s theorem is in some sense “commutative,” since it concerns the abelian Lie group GL(1,C), whereas Grauert’s theorem concerns the nonabelian groups GL(n,C). But there are further extensions of both theorems into the realm of noncommutative geometry (in the sense of Alain Connes), and as I shall explain these extensions have interesting links to representation theory.


May 26 DT Seminar 
15:00  16:30 Sci 6609 
Ryunosuke Ozawa (Kyoto)
測度距離空間の列の相転移性質


June 09 
15:00  16:30 RIMS 206 
Koichi Shimada (Tokyo)
Approximate Unitary Equivalence of Finite Index Endomorphisms of the AFD Factors
We characterize the condition for two finite index endomorphisms on an AFD factor to be mutually approximately unitarily equivalent. The characterization is given by using the canonical extension of endomorphisms, which is introduced by Izumi. Our result is a generalization of the characterization of approximate innerness of endomorphisms of the AFD factors, obtained by KawahiashiSutherlandTakesaki and MasudaTomatsu. Our proof, which does not depend on the types of factors, is based on recent development on the Rohlin property of flows on von Neumann algebras.


June 1119 SGU Lecture 
Sci 3127 
Vaughan F. R. Jones (Vanderbilt/Kyoto)
An introduction to subfactors in mathematics and physics.
11(T) 10:00  12:00, 12(F) 10:00  12:00, 15(M) 15:00  17:00, 17(W) 10:00  12:00, 19(F) 10:00  12:00.
Short Abstract.
We will introduce the theory of subfactors and their interactions with
topology and physics.
Goal.
We intend to describe the current state of classification of subfactors and attack the question of whether all subfactors have something to do with quantum field theory, including an appearance of Richard Thompson’s groups F and T.
Plan of the lectures.
Lecture 1.
Introduction to von Neumann algebras. Definition and examples. Von Neumann density theorem. Factors of types I,II and III. TomitaTakesaki theory and Connes decomposition and classification. Hyperfiniteness.
Lecture 2.
Subfactors and elementary examples. Index in the type II case. Bimodules. The tower of relative commutants and restrictions on index values. Construction of examples. Braid group representations and knot polynomials.
Lecture 3.
Kauffman diagrams for the TemperleyLieb algebra. Planar algebras, lambda lattices  the standard invariant of a subfactor and reconstruction. Random matrices with a real number of matrices. Tensor categories, 2categories. Endomorphisms and the type III approach.
Lecture 4.
Classification of small index subfactors. Izumi’s Cuntz algebra approach. Skein theory presentations of subfactors, the exchange relation, the YangBaxter equation and the jellyfish algorithm.
Lecture 5.
Algebraic quantum field theory, conformal field theory and scaling limits of statistical mechanical models. Hilbert spaces from planar algebrasa toy algebraic QFT and the Thompson groups. Knots and links from the Thompson groups.
Prerequisites: Some functional analysisincluding the spectral theorem on Hilbert space. Some topology including the fundamental group and homology groups. Some quantum mechanics including the Schrodinger equation and the uncertainty principle.


June 2728 
Sendai 
Takagi Lectures


June 30 
15:00  16:30 RIMS 206 
Reiji Tomatsu (Hokkaido)
PopaVaesのC*tensor categoryの表現論の紹介．


July 03 SGU Seminar 
14:45  16:15 Sci 3127 
Vaughan F. R. Jones (Vanderbilt/Kyoto)
Knots and Braids (Introductory Lecture)


July 07 
15:00  16:00 RIMS 206 
Pinhas Grossman (UNSW Australia)
Some examples of fusion categories associated to finite groups and to subfactors
A fusion category is a tensor category that “looks like” the category of representations of a finite group. Fusion categories arise as categories of bimodules or endomorphisms associated to finite depth subfactors.
In this talk we will explain some representation theory of fusion categories by looking at examples of fusion categories associated to some small groups, as well as fusion categories associated to certain subfactors which are related to those groups.


16:15  17:15 RIMS 206 
David Penneys (UCLA)
Bicommutant categories
I'll discuss an ongoing joint project with Andre Henriques. Just as a tensor category is a categorification of a ring, and its Drinfel'd
center is a categorification of the center of a ring, a bicommutant category is a categorification of a von Neumann algebra. I'll define
the notion of the commutant C' of a tensor category C inside an ambient tensor category B. A bicommutant category is then a category which is equivalent to its own bicommutant inside B.
Because we are interested in von Neumann algebras, we work in the ambient category B=Bim(R), the tensor category of bimodules over a hyperfinite von Neumann factor R, which can be thought of as a categorification of B(H). Given a unitary fusion category C inside Bim(R), we identify its bicommutant C'', which we show is, in fact, an example of a bicommutant category. Along the way, we provide machinery for constructing elements of C', and we see the LongoRehren subfactor appear naturally.


July 21 
15:00  16:30 RIMS 206 
Mikael Pichot (McGill)
TBA


Aug. 1921 
RIMS 111 
Recent developments in operator algebras
(program)


Aug. 28 Friday 
15:00  16:30 RIMS 206 
Gilles Godefroy (Paris)
TBA
tba


Sep. 0811 
Sci 3110 
Group Actions and Metric Embeddings


Oct. 2426 
MyoKo 
Annual meeting on operator theory & operator algebra theory

