School of Mathematics and Statistics

Dr Joachim Zacharias

  • Reader (Mathematics)

email: Joachim.Zacharias@glasgow.ac.uk


Research Interests

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).                                                                 
                     

Research Groups

Jump to: 2013 | 2010 | 2009 | 2008 | 2006 | 2005 | 2003 | 2001 | 2000
Number of items: 19.

2013

Hawkins, A., Skalski, A., White, S., and Zacharias, J. (2013) On spectral triples on crossed products arising from equicontinuous actions. Mathematica Scandinavica . ISSN 0025-5521 (In Press)

2010

Winter, W., and Zacharias, J. (2010) The nuclear dimension of C*-algebras. Advances in Mathematics, 224 (2). pp. 461-498. ISSN 0001-8708 (doi:10.1016/j.aim.2009.12.005)

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. ISSN 0024-6107 (doi:10.1112/jlms/jdq023)

Skalski, A., and Zacharias, J. (2010) On approximation properties of Pimsner algebras and crossed products by Hilbert bimodules. Rocky Mountain Journal of Mathematics, 40 (2). pp. 609-625. ISSN 0035-7596

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. ISSN 0379-4024

2009

Skalski, A., and Zacharias, J. (2009) A note on spectral triples and quasidiagonality. Expositiones Mathematicae, 27 (2). pp. 137-141. ISSN 0723-0869 (doi:10.1016/j.exmath.2008.10.007)

Winter, W., and Zacharias, J. (2009) Completely positive maps of order zero. Munster Journal of Mathematics, 2 . pp. 311-324. ISSN 1867-5778

2008

Skalski, A., and Zacharias, J. (2008) Entropy of shifts on higher-rank graph C<sup>*<sup>-algebras. Houston Journal of Mathematics, 34 (1). pp. 269-282. ISSN 0362-1588

Skalski, A., and Zacharias, J. (2008) Noncommutative topological entropy of endomorphisms of Cuntz algebras. Letters in Mathematical Physics, 86 (2-3). pp. 115-134. ISSN 0377-9017 (doi:10.1007/s11005-008-0279-y)

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. ISSN 0129-167X (doi:10.1142/S0129167X08004765)

2006

Bhat, B.V.R., Dey, S., and Zacharias, J. (2006) Minimal Cuntz-Krieger dilations and representations of Cuntz-Krieger algebras. Proceedings Mathematical Sciences, 116 (2). pp. 193-220. ISSN 0253-4142 (doi:10.1007/BF02829787)

2005

Popescu, I., and Zacharias, J. (2005) E-theoretic duality for higher rank graph algebras. K-Theory, 34 (3). pp. 265-282. ISSN 0920-3036 (doi:10.1007/s10977-005-5544-6)

Zacharias, J. (2005) Topological entropy of quotients and extensions. In: Schurmann, M. and Franz, U. (eds.) Quantum Probability and Infinite Dimensional Analysis: From Foundations to Applications. Series: QP-PQ, quantum probability and white noise analysis (18). World Scientific, pp. 525-535. ISBN 9789812561473

2003

Hirshberg, I., and Zacharias, J. (2003) On the structure of spectral algebras and their generalizations. In: Price, G.L. (ed.) Advances in Quantum Dynamics. Series: Contemporary mathematics (335). American Mathematical Society, Providence, R.I., pp. 149-163. ISBN 9780821832158

2001

Zacharias, J. (2001) Endomorphisms of continuous Cuntz algebras. Journal of Operator Theory, 46 (3). pp. 561-577. ISSN 0379-4024

Zacharias, J. (2001) Splitting for subalgebras of tensor products. Proceedings of the American Mathematical Society, 129 (2). pp. 407-413. ISSN 0002-9939

2000

Zacharias, J. (2000) Pure infiniteness of spectral algebras. Journal of Functional Analysis, 178 (2). pp. 381-395. ISSN 0022-1236 (doi:10.1006/jfan.2000.3661)

Zacharias, J. (2000) Continuous Tensor Products and Arveson's Spectral C*-algebras. Series: Memoirs of the American Mathematical Society, 680 . American Mathematical Society, Providence (R.I.). ISBN 9780821815458

Zacharias, J. (2000) Quasi free automorphisms of Cuntz-Krieger-Pimsner-algebras. In: Cuntz, J. and Echterhoff, S. (eds.) C*-algebras: Proceedings of the SFB-Workshop on C*-Algebras, Münster, Germany, March 8-12, 1999. Springer, Berlin, pp. 262-272. ISBN 9783540675624

This list was generated on Tue Oct 1 15:20:44 2013 BST.

Current PhD students

Gabriel Tornetta (Bivariant Cuntz Semigroup )