Dr Joachim Zacharias

  • Reader (Mathematics)

telephone: 01413306060
email: Joachim.Zacharias@glasgow.ac.uk

School of Math & Stats
15 University Gardens
G128qw

Research interests

Personal website

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


Publications

All publications | View selected publications

List all by: Type | Date

Jump to: 2017 | 2016 | 2015 | 2013 | 2010 | 2009 | 2008 | 2006 | 2005 | 2003 | 2001 | 2000
Number of items: 24.

2017

Szabo, G., Wu, J. and Zacharias, J. (2017) Rokhlin dimension for actions of residually finite groups. Ergodic Theory and Dynamical Systems, (Accepted for Publication)

Hawkins, A. and Zacharias, J. (2017) Spectral metric spaces on extensions of C*-algebras. Communications in Mathematical Physics, 350(2), pp. 475-506. (doi:10.1007/s00220-016-2820-7)

2016

Bosa, J., Tornetta, G. and Zacharias, J. (2016) Open projections and suprema in the Cuntz semigroup. Mathematical Proceedings of the Cambridge Philosophical Society, (doi:10.1017/S030500411600089X) (Early Online Publication)

2015

Hirshberg, I., Winter, W. and Zacharias, J. (2015) Rokhlin dimension and C*-dynamics. Communications in Mathematical Physics, 335(2), pp. 637-670. (doi:10.1007/s00220-014-2264-x)

Bhowmick, J., Voigt, C. and Zacharias, J. (2015) Compact quantum metric spaces from quantum groups of rapid decay. Journal of Noncommutative Geometry, 9(4), pp. 1175-1200. (doi:10.4171/JNCG/220)

2013

Hawkins, A., Skalski, A., White, S. and Zacharias, J. (2013) On spectral triples on crossed products arising from equicontinuous actions. Mathematica Scandinavica, 113(2), pp. 262-291.

2010

Winter, W. and Zacharias, J. (2010) The nuclear dimension of C*-algebras. Advances in Mathematics, 224(2), pp. 461-498. (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. (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.

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.

2009

Skalski, A. and Zacharias, J. (2009) A note on spectral triples and quasidiagonality. Expositiones Mathematicae, 27(2), pp. 137-141. (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.

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.

Skalski, A. and Zacharias, J. (2008) Noncommutative topological entropy of endomorphisms of Cuntz algebras. Letters in Mathematical Physics, 86(2-3), pp. 115-134. (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. (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. (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. (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 (doi:10.1090/conm/335)

2001

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

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

2000

Zacharias, J. (2000) Pure infiniteness of spectral algebras. Journal of Functional Analysis, 178(2), pp. 381-395. (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 Wed Nov 22 11:48:57 2017 GMT.
Number of items: 24.

Articles

Szabo, G., Wu, J. and Zacharias, J. (2017) Rokhlin dimension for actions of residually finite groups. Ergodic Theory and Dynamical Systems, (Accepted for Publication)

Hawkins, A. and Zacharias, J. (2017) Spectral metric spaces on extensions of C*-algebras. Communications in Mathematical Physics, 350(2), pp. 475-506. (doi:10.1007/s00220-016-2820-7)

Bosa, J., Tornetta, G. and Zacharias, J. (2016) Open projections and suprema in the Cuntz semigroup. Mathematical Proceedings of the Cambridge Philosophical Society, (doi:10.1017/S030500411600089X) (Early Online Publication)

Hirshberg, I., Winter, W. and Zacharias, J. (2015) Rokhlin dimension and C*-dynamics. Communications in Mathematical Physics, 335(2), pp. 637-670. (doi:10.1007/s00220-014-2264-x)

Bhowmick, J., Voigt, C. and Zacharias, J. (2015) Compact quantum metric spaces from quantum groups of rapid decay. Journal of Noncommutative Geometry, 9(4), pp. 1175-1200. (doi:10.4171/JNCG/220)

Hawkins, A., Skalski, A., White, S. and Zacharias, J. (2013) On spectral triples on crossed products arising from equicontinuous actions. Mathematica Scandinavica, 113(2), pp. 262-291.

Winter, W. and Zacharias, J. (2010) The nuclear dimension of C*-algebras. Advances in Mathematics, 224(2), pp. 461-498. (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. (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.

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. (2009) A note on spectral triples and quasidiagonality. Expositiones Mathematicae, 27(2), pp. 137-141. (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.

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.

Skalski, A. and Zacharias, J. (2008) Noncommutative topological entropy of endomorphisms of Cuntz algebras. Letters in Mathematical Physics, 86(2-3), pp. 115-134. (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. (doi:10.1142/S0129167X08004765)

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. (doi:10.1007/BF02829787)

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

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

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

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

Books

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

Book Sections

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

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 (doi:10.1090/conm/335)

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 Wed Nov 22 11:48:57 2017 GMT.

Grants


Supervision

Current research staff

Joan Bosa

Current PhD students

Luke Hamblin
Dimitrios Gerontogiannis


Teaching


Additional information