Dr Joachim Zacharias
- Reader (Mathematics)
School of Math & Stats
15 University Gardens
My research interests are in C*-algebras and their applications. C*-algebras and their measure theoretical counterpart, von Neumann algebras, are algebras of operators on a Hilbert space. They were first motivated by quantum theory and occurred in group representations and ergodic theory. They can also be characterised abstractly as Banach algebras by a very natural norm condition. The understanding of C*-algebras and von Neumann algebras has seen remarkable progress in the past decades which has lead to far reaching classification results using methods originally developed in topology, notably K-theory. C*-algebras have occurred in many other branches of mathematics. C*-algebra theory is a rapidly growing field with many exiting open problems and many possible PhD projects. I am particularly interested in classification of simple nuclear C*-algebras, non commutative dimension concepts, dynamical systems, special examples of C*-algebras, in particular the very rich class of Cuntz algebras and various generalisations (graph, Pimsner, higher rank, continuous etc.), K-theory for those C*-algebras, approximation properties of C*- and von Neumann algebras, dynamical systems and their applications to C*-algebras, noncommutative geometry (spectral triples).
Selected publications | View all publications
Skalski, A. and Zacharias, J. (2010) Approximation properties and entropy estimates for crossed products by actions of amenable discrete quantum groups. Journal of the London Mathematical Society, 82(1), pp. 184-202. (doi:10.1112/jlms/jdq023)
Skalski, A. and Zacharias, J. (2010) Poisson transform for higher-rank graph algebras and its applications. Journal of Operator Theory, 63(2), pp. 425-454.
Skalski, A. and Zacharias, J. (2008) Wold decomposition for representations of product systems of C* corrrespondences. International Journal of Mathematics, 19(4), pp. 455-479. (doi:10.1142/S0129167X08004765)