Research group
Geometry and Operator Algebras
We are delighted to invite you to the Banach Center series of lectures by
ERIK CHRISTENSEN (University of Copenhagen):
17 November 2008 Monday 10:15 - 11:45
Instytut Matematyczny PAN, Śniadeckich 8, room 322
DEGENERATION OF NON-COMMUTATIVE COMPACT METRIC SPACES
Given a spectral triple associated to a unital C*-algebra and an extension
of the C*-algebra by the compacts, we construct a 2-parameter family of
spectral triples associated to the extended C*-algebra. In this way we
obtain a two-parameter family of noncommutative compact metric spaces. By
a variation of the parameters, we can obtain the compacts as well as the
original C*-algebra as degeneration limits in the sense of noncommutative
compact metric spaces. This is a joint work with Cristina Ivan, Hannover.
17 November 2008 Monday 14:15 - 15:00 and 15:15 - 16:00
Instytut Matematyczny PAN, Śniadeckich 8, room 322
APPLICATIONS OF THE CLASSIFICATION PROGRAM FOR C*-ALGEBRAS TO THE THEORY
OF PERTURBATIONS OF C*-ALGEBRAS
The classification program provides results which tell that for certain
classes of C*-algebras there is a complete set of invariants, such as
K-groups, traces and the pairing of the traces with K0. For the
perturbation question, we consider two subalgebras of a common bigger
C*-algebra, and we say that the algebras are close if their unit balls are
close in the Hausdorff metric induced by the norm. One question is then if
algebras that are sufficiently close are isomorphic. A way to a positive
answer is to show that the invariants used in the classification results
are stable under small perturbations of algebras. We give some positive
answers to questions of this type. This is a joint work with Allan
Sinclair, Edinburgh, Roger Smith, Texas, and Stuart White, Glasgow.
18 November 2008 Tuesday 12:00 - 13:30
Instytut Matematyki UW, ul. Banacha 2, room 5870
FRACTALS STUDIED VIA NONCOMMUTATIVE GEOMETRY
A fractal set, such as the Cantor set or the Sierpinski gasket, is by no
means smooth. Anyway, the theory developed to describe noncommutative
smooth manifolds can be applied in this setting, and we can recover
geodesic distances, Minkowski dimensions, Hausdorff measures and elements
of K-homology in this way. The results are obtained in collaboration with
Cristina Ivan, Hannover.
Piotr M. Hajac, Stefan Jackowski, and Stanisław L. Woronowicz