Joachim Zacharias 

Reader in Mathematics 

School of Mathematics and Statistics 

University of Glasgow 

Mathematics Building 

Office 334 

e-mail: Joachim.Zacharias.at.glasgow.ac.uk

Teaching (2017/18)

• Math 2D, Topics in Calculus and Linear Algebra (semester 2) 
• Math 4H, Functional Analysis 

Research Interests

• C*-Algebras 
• Ergodic Theory, Entropy and Dynamical Systems 
• Operator Theory related to Completely Positive Maps 
• Approximation Properties of Algebras and Groups 
• Coarse and Noncommutative Geometry 

Publications/Preprints

You can find most of my publications/preprints (except the earlier ones) in their current versions on the arXiv. 

• [1] Continuous tensor products and Arveson’s spectral algebras, 122pp. memoir AMS vol.143, No.680 (2000) 
• [2] Splitting for subalgebras of tensor products, Proceedings AMS Vol.129, No.2, 407–413 (2000) 
• [3] Endomorphisms of continuous Cuntz algebras, Journal of Op. Theory Vol.46, No.3, 560–579, (Supplement 2001) 
• [4] Quasi-free automorphisms of Cuntz-Krieger-Pimsner-algebras, C*-algebras Munster 1999, Cuntz/Echterhoff editors, 262–272 Springer (2000) 
• [5] Pure infiniteness of continuous Cuntz algebras, Journal of Functional Analysis Vol.178, 381–396 (2000) 
• [6] On the structure of spectral algebras and their generalizations, (coauthor Ilan Hirshberg) Contemporary Mathematics 335, 149–163, (2003) 
• [7] Topological entropy of quotients and extensions, D. F. Parker and G. A. Maugin (editors), Quantum Probability and Infinite Dimensional Analysis, 22-28 June 2003, Greifswald, 525–535, (2005) 
• [8] E-theoretic duality for higher rank graph algebras, (coauthor Iulian Popescu), K-Theory 34 (no. 3), 265–282, (2005) 
• [9] On the invariant translation approximation property for discrete groups, Proceedings AMS 134, 1909–1916, (2006) 
• [10] Minimal Cuntz-Krieger dilations and representations of Cuntz-Krieger algebras, (coauthors B. V. R. Bhat and S. Dey), Proc. Indian Acad. Sci. Math. Sci. 116 (2006), no. 2, 193–220 
• [11] Entropy of shifts on higher-rank graph C∗-algebras, (coauthor Adam Skalski), Houston Journal Math. 34, 269–282, (2008) 
• [12] Wold decomposition for representations of product systems of C∗-algebras, (coauthor Adam Skalski), Int. Journal Math. 19, 455–479, (2008) 
• [13] Noncommutative topological entropy of endomorphisms of Cuntz algebras, (coauthor Adam Skalski), Letters in Math. Phys. 86, 115-134, (2008) 
• [14] A note on spectral triples and quasidiagonality, (coauthor A. Skalski), Expositiones Math. 27, 137-141 (2009) 
• [15] Completely positive maps of order zero, (coauthor W. Winter), Mu ̈nster Journal of Math. 2, 311-324, (2009) 
• [16] The nuclear dimension of C*-algebras, (coauthor W. Winter), Advances in Math. 224, 461-498 (2010) 
• [17] On approximation properties of crossed products by Hilbert bimodules, (coauthor Adam Skalski), Rocky Mountain J. Math. 40, 609-625 (2010) 
• [18] Poisson transform for higher rank graph algebras and its applications, (coauthor Adam Skalski), J. Operator Th. 63, 425-454 (2010) 
• [19] Approximation properties and entropy estimates for crossed products by actions of amenable quantum groups, (coauthor Adam Skalski), Journal of the LMS 82, 184-202 (2010) 
• [20] On spectral triples on crossed products arising from equicontinuous actions, Mathematica Scandinavica, 113 (2), 262-291 (2013) (coauthors: A. Hawkins, A. Skalski und S. White) 
• [21] Rokhlin dimension and C*-dynamics, Communications in Mathematical Physics 335 (2), 637-670, (2015), (coauthors: I. Hirshberg und W. Winter) 
• [22] Compact quantum metric spaces from quantum groups of rapid decay, Journal of Noncommutative Geometry, Vol. 9 (4), 1175-1200, (2015), (coauthors: J. Bhowmick und Christian Voigt) 
• [23] Spectral metric spaces on extensions of C*-algebras, Com. Math. Phys. 350, Issue 2, 475–506,(2017), (coauthor A. Hawkins) 
• [24] Rokhlin dimension for actions of residually finite groups, (coauthors: G. Szabo und J. Wu), 65 pages, to appear in Ergodic Theory and Dyn Systems (2017) 
• [25] Open projections and suprema in the Cuntz semigroup, Mathematical Proceedings of the Cambridge Philosophical Society (First view, electronic), 1-12, (2016) (coauthors: J. Bosa und G. Tornetta) 
• [26] A bivariant theory for the Cuntz semigroup, preprint math.OA1602.02043, 37pp, (2016), (coauthors: J. Bosa und G. Tornetta) 
• [27] The Fubini product and its applications, preprint math.OA1603.04527, 17pp, (2016) (coauthor: Otgonbayar Uuye) 

Selected Seminars and Conferences

• 2006 Newcastle, Southampton, London Imperial, Belfast, Orleans, Munster, Leeds 
• 2007 Paris, Lancaster, Toronto, Glasgow 
• 2008 Cork, Munster, Odense 
• 2009 Aberystwyth, Munster, Southampton 
• 2010 Bangalore (ICM Satellite), Bedlewo 
• 2011 Swansea, Belfast, Barcelona, Kopenhagen, Warsaw 
• 2012 London, Edinburgh, Aberystwyth, Sheffield, Oberwolfach, Kyoto 
• 2013 Aberdeen, Berkeley, Madrid, Munster 
• 2014 Bonn, Warsaw, Copenhagen 
• 2015 London, Shanghai, Abel Symposium (Norway), Wabash Seminar (Indianapolis), Purdue, Hawai, Munster 
• 2016 Stockholm (Mittag-Leffler Institute), Beijing, Bedlewo, Warsaw (Senior Simons Professor) 
• 2017 Glasgow, Barcelona, Banff, Sheffield, Trieste, Oberwolfach 
• Several upcoming events this and next year. 

Masterclass lecturer in Budapest, Madrid and Warsaw 

Grants/Service

• Holder or joint holder of numerous research grants between 2003 and 2016 (total volume £531.750) 
• Part of numerous EU and non-EU networks 
• Extensive refereeing for journals and research grant applications 
• External examiner for PhDs in Belfast und Newcastle, Sheffield, Nijmegen, Barcelona 

Conference and Seminar Organisation

• 2003, 2006 und 2010 North British Functional Analysis Seminar in Nottingham 
• 2006 Quantum Probability Information and Control (QPIC) Symposium in Nottingham (main organiser) 
• 2007 Fields Institute Workshop in Noncommutative Dynamics (with Remus Floricel) 
• 2010 LMS regional Meeting and Workshop: C*-Algebras and their Classification, Nottingham 6-10/9/2010 (with W. Winter) 
• 2007-2011 Organisor of the Analysis und Operator Algebra Seminar in Nottingham 
• 2009-2012 Secretary of the North British Functional Analysis Seminar (NBFAS). 
• 2011-2012 Seminar network in operator algebras and noncommutative geometry, (with M.Daws (Leeds) and P. Mitchner (Sheffield)). 
• 2014 Conference and Masterclass CSTAR, Glasgow 25-29 Aug, 1-5 Sept, 2014. 

PhD Students

• Iulian Popescu (title: ‘Duality for higher rank graph algebras’, 2002-2005) 
• Adam Skalski (supervisor only during last year 2005-2006, title: ‘Quantum stochastic convolution cocycles’) 
• Christina Cerny (title: ‘On higher rank Cuntz-Pimsner algebras’, 2007-2012) 
• Andrew Hawkins (title: ‘Construction of spectral triples on C*-algebras’, 2009-2013) 
• Gabriele Tornetta (title: ‘A Bivariant Theory for the Cuntz Semigroup and its Role for the Classification Programme of C*-Algebras’, 2012-2016) 
• Luke Hamblin (jointly with Mike Whittaker, since October 2015, Topic: Rokhlin dimension, wraped cones and amenability dimension) 
• Dimitrios Gerontogiannis (jointly with Mike Whittaker, since October 2016, Topic: K-homology and noncommutative Poincare duality) 

Post docs

• Adam Skalski (2006-2007, EPSRC) 
• Joan Bosa (2013-2015, EPSRC, 2015-2017 Catalan grant)