# Kyoto Operator Algebra Seminar

Organizers: Masaki IZUMI, Narutaka OZAWA, Yoshikata KIDA
Time and Location: 15:00 - 16:30 on Tuesday at RIMS 006
Seminar Description: This seminar features both research and introductory talks on topics in Operator Algebra, Noncommutative Geometry, Ergodic Theory, and Group Theory of various kinds (geometric, measure theoretic, functional analytic, etc.). The talks are informal and take between an hour and an hour and a half.
Useful Tips: How to Give a Good Colloquium. Advice on Giving Talks (Upgrade). Myths.
Memento: 2011  2012  2013

## 2014 Spring/Summer

 Mar. 24 Monday 10:30 - 12:00 RIMS 110 Detlev Buchholz (Göttingen) Quantum systems and resolvent algebras The standard $\mathrm{C}^*$-algebraic version of the Heisenberg algebra of canonical commutation relations, the Weyl algebra often causes difficulties since it does not admit physically interesting dynamical laws as automorphism groups. In this talk a $\mathrm{C}^*$-algebraic version of the canonical commutation relations is presented which circumvents such problems. It is based on the resolvents of the canonical operators and their algebraic relations. The resulting $\mathrm{C}^*$-algebras, the resolvent algebras, have many desirable analytic properties. In fact, they are of type I (postliminal) for finite quantum systems and nuclear in the infinite case. In either case they admit existence of an abundance of one--parameter automorphism groups corresponding to physically relevant dynamics. They are also useful in the discussion of supersymmetry and systems with constraints. Moreover, the resolvent algebras have a rich and interesting ideal structure which encodes specific information about the dimension of the underlying physical system. They thus provide an excellent framework for the rigorous analysis of finite and infinite quantum systems. Apr. 22 15:00 - 16:30 RIMS 006 Benoit Collins (Kyoto) Describing exchangeable SU(n) invariant separable states In quantum information theory, a state is a positive matrix in $M_n({\mathbb C})$ of trace $1$. In a tensor product (multipartite system), a state is called separable iff it is the convex combination of tensor product states. In $M_n({\mathbb C})^{\otimes k}$, we are interested in the problem of describing the convex body of separable states who are $\mathrm{SU}(n)$ invariant (with respect to the diagonal action), and exchangeable (i.e. invariant under the canonical action of the permutation group on k points). This problem arises from quantum information theory, where the notion of separable state is seen as the negation of the crucial notion of entangled state. It turns out that this problem admits a nice solution through the study of Martin boundary of random walks on Bratelli diagrams. Joint work in preparation with M. Al Nuwairan and T. Giordano. May 13 15:00 - 16:30 RIMS 006 Norio Nawata (Osaka Kyoiku) TBA tba May 20 15:00 - 16:30 RIMS 006 Masato Mimura (Tohoku) TBA tba May 27 15:00 - 16:30 RIMS 006 Ion Nechita (Toulouse) TBA tba June 03 15:00 - 16:30 RIMS 006 TBA TBA tba June 17 15:00 - 16:30 RIMS 006 TBA TBA tba June 24 15:00 - 16:30 RIMS 006 Yusuke Isono (Kyoto) TBA tba July 01 DG Seminar 15:00 - 16:30 Sci 6-609 Yoshikata Kida (Kyoto) TBA tba July 08 15:00 - 16:30 RIMS 006 TBA (tba) TBA tba July 15 15:00 - 16:30 RIMS 006 TBA (tba) TBA tba July 19-22 Otaru Summer Camp on Operator Algebras Sep. 08-10 RIMS 420 Recent Developments in Operator Algebras (program (tba))

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