Professor Joachim Zacharias

Professor (Mathematics)

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

School of Math & Stats, 15 University Gardens, G128qw

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

Analysis

Publications

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Number of items: 29.

2024

Gerontogiannis, D. M., Whittaker, M. F. and Zacharias, J. (2024) A geometric representative for the fundamental class in KK-duality of Smale spaces. Journal of Functional Analysis, 287(2), 110455. (doi: 10.1016/j.jfa.2024.110455)

2020

Uuye, O. and Zacharias, J. (2020) The Fubini product and its applications. Bulletin of the Malaysian Mathematical Sciences Society, 43(6), pp. 4041-4061. (doi: 10.1007/s40840-020-00909-8)

Easo, P. et al. (2020) The Cuntz-Toeplitz algebras have nuclear dimension one. Journal of Functional Analysis, 279(7), 108690. (doi: 10.1016/j.jfa.2020.108690)

2019

Bosa, J., Tornetta, G. and Zacharias, J. (2019) A bivariant theory for the Cuntz semigroup. Journal of Functional Analysis, 277(4), pp. 1061-1111. (doi: 10.1016/j.jfa.2019.05.002)

Szabo, G., Wu, J. and Zacharias, J. (2019) Rokhlin dimension for actions of residually finite groups. Ergodic Theory and Dynamical Systems, 39(8), pp. 2248-2304. (doi: 10.1017/etds.2017.113)

2018

Bosa, J., Tornetta, G. and Zacharias, J. (2018) Open projections and suprema in the Cuntz semigroup. Mathematical Proceedings of the Cambridge Philosophical Society, 164(1), pp. 135-146. (doi: 10.1017/S030500411600089X)

Cave, C. and Zacharias, J. (2018) Kirchberg-Wassermann exactness vs exactness: reduction to the unimodular totally disconnected case. Münster Journal of Mathematics, 11, pp. 217-224. (doi: 10.17879/87109577544)

2017

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)

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 Thu Nov 21 01:57:55 2024 GMT.

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