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


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

