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 oneparameter 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 6609 
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 1922 
Otaru 
Summer Camp on Operator Algebras


Sep. 0810 
RIMS 420 
Recent Developments in Operator Algebras (program (tba))

