Professor David E Evans
Overview
Telephone: +44(0)29 208 74522
Fax: +44(0)29 208 74199
Extension: 74522
Location: M/2.39
Research Interests
David E Evans has published with Yasuyuki Kawahigashi a monograph Quantum Symmetries on Operator Algebras  the combinatorial and physical aspects of operator algebras (see here for the list of updates/corrections). This is a continuation of the work of Evans in his previous collaborations with Araki and Lewis on a C*algebra approach to phase transitions in the twodimensional Ising model. Evans also has interests in the study of amenable C*algebras by K theoretic or topological invariants, e.g. the expression of finite amenable simple C* algebras as the inductive limit of simpler building blocks  Elliott and Evans expressed the irrational rotation algebras as inductive limits of circle algebras. There is much interchange of ideas from amenable subfactors and amenable C*algebras in this work (e.g. through common ideas from orbifolds and Rokhlin properties of automorphisms). Recent work has focused on the study of modular invariant partition functions through subfactors and twisted equivariant Ktheory – the latter being a programme of research with Terry Gannon.
Research Group
Mathematical Physics (Noncommutative Geometry)
Recent Significant Publications
(With T. Gannon). Modular invariants and Twisted Equivariant Ktheory. Commun. Number Theory Phys., 3 (2009), 209296. arXiv:0807.3759[math.KT]
(With M. Pugh). Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory. Commun. Math. Phys., 295 (2010) 363413. arXiv:0906.4314[math.OA]
(With T. Gannon). The exoticness and realisability of the HaagerupIzumi modular data. Commun. Math. Phys., to appear. arXiv:1006.1326[math.QA]
(With T. Gannon). Modular invariants and Twisted Equivariant Ktheory II: Dynkin diagram symmetries. arXiv:1012.1634[math.KT]
Administrative Duties
Mathematical Physics Seminar Organiser
London Mathematical Society Liaison
Welsh Liaison Officer
Member of School Research Committee
Member of School REF Committee
Coordinator of EU Network – EUNCNG
Operator Algebras Seminar Organiser
Coordinator of EPSRC Network  ABCKLM
Wales Mathematics Video Seminars
WIMCS Mathematical Physics Cluster Manager
Member of WIMCS Research Committee
Personal Website
Publications

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ArVix
Video Talks
 Subfactors and Algebraic Aspects of Quantum Field Theory, MSRI Berkeley December 2000
Modular invariants from Subfactors
Algebraic Quantum Field Theory – the first 50 Years, Gottingen July 2009
Operator Algebras: Impact of AQFT on Subfactors and Ktheory
Shanks Workshop "Conformal Field Theory and Von Neumann Algebras''
Vanderbilt, October 2011.
The search for the exotic  subfactors and conformal field theories
Recent Publications
Selected publications prior to 1996, are available on my personal website.
 (With G.A. Elliott, H. Su). Classification of inductive limits of matrix algebras over the Toeplitz algebra. In Operator Algebras and Quantum Field Theory, (ed. S. Doplicher et al), International Press, 1998.
 (With Y. Kawahigashi). Quantum Symmetries on Operator Algebras pp 848 + xv, Oxford University Press 1998. Updates/Corrections
 (With O. Bratteli, G.A. Elliott, A. Kishimoto). On the classification of C*algebras of real rank zero, III: the infinite case. In Operator algebras and their applications. Fields Institute Communications, American Mathematical Society. 20 (1998) 1172.
 (With O. Bratteli, G.A. Elliott, A. Kishimoto). Homotopy of a pair of commuting unitaries in a simple C*algebra. Journ. Functional Analysis 160 (1998) 466523.
 (With G.A. Elliott, A. Kishimoto). Outer conjugacy classes of trace scaling automorphisms of stable UHF algebras. Math. Scand. 83 (1998) 7486.
 (With A. Kishimoto). Trace scaling automorphisms of certain stable AF algebras. Hokkaido Math. J., 26 (1997), 211224.
 (With Y. Kawahigashi). Orbifold subfactors from Hecke algebras II: quantum double and braiding. Commun. Math. Phys. 196 (1998) 331361, functan/9702018.
 The Rohlin property and classification of trace scaling automorphisms of AF algebras. In Operator Algebras and Quantum Field Theory, (ed. S. Doplicher et al), 123135, International Press, 1998.
 (With O. Bratteli, P.E.T. Jorgensen). Compactly supported wavelets and representations of the Cuntz relations. Applied and Computational Harmonic Analysis 8 (2000) 166196.
 (With J.Boeckenhauer). Modular invariants, graphs and alphainduction for nets of subfactors I. Commun. Math. Phys. 197 (1998) 361386, hepth/9801171.
 (With J.Boeckenhauer). Modular invariants, graphs and alphainduction for nets of subfactors II. Commun. Math. Phys. 200 (1999) 57103, hepth/98005023.
 (With J.Boeckenhauer). Modular Invariants, graphs and alphainduction for Nets of Subfactors III. Commun. Math. Phys. 205 (1999) 183228, hepth/9812110.
 (With J.Boeckenhauer, Y. Kawahigashi). On alphainduction, chiral projectors, and modular invariants for subfactors. Commun. Math. Phys. 208 (1999) 429487, math.OA/9904109
 (With J.Boeckenhauer, Y. Kawahigashi). Chiral structure of modular invariants for subfactors. Commun. Math. Phys. 210 (2000) 733784, math.OA/9907149.
 (With J.Boeckenhauer, Y. Kawahigashi). LongoRehren subfactors arising from alphainduction. Publ. RIMS Kyoto37 (2001) 135, math.OA/0002154.
 (With J.Boeckenhauer). Modular invariants from subfactors: Type I coupling matrices and intermediate subfactors. Commun. Math. Phys. 213 (2000) 267289, math.OA/9911239.
 (With J.Boeckenhauer). Modular invariants from subfactors. In Quantum Symmetries in Theoretical Physics and Mathematics (Bariloche, 2000), 95131, Contemp. Math., 294, Amer. Math. Soc., Providence, RI, 2002, math.OA/0006114.
 (With J.Boeckenhauer). Modular Invariants and subfactors. In Mathematical physics in mathematics and physics (Siena, 2000), 1137, Fields Inst. Commun., 30, Amer. Math. Soc., Providence, RI, 2001, math.OA/0008056.
 From XY to ADE. In Geometric analysis and applications (Canberra, 2000), 85105, Proc. Centre Math. Appl. Austral. Nat. Univ., 39, Austral. Nat. Univ., Canberra, 2001.
 Fusion rules of modular invariants. Reviews in Math. Physics, 14 (2002) 709732, math.OA/0204278
 Critical Phenomena, modular invariants and operator algebras. In Operator algebras and mathematical physics (Constanta, 2001, J.Cuntz, G.A.Elliott, S. Stratila et el. eds.), The Theta Foundation, Bucharest, 2003. math.OA/0204281
 (With P.R. Pinto). Modular invariants and their fusion rules. In Advances in Quantum Dynamics (Mount Holyoke 2002), Contemp. Math. Amer. Math. 335 (2003) 119130, Providence, RI, Amer. Math. Soc., math.OA/0309175.
 (With P.R. Pinto). Subfactor realisation of modular invariants. Commun. Math. Phys. 237 (2003) 309363, math.OA/0309174.
 (With R. E. Behrend). Integrable lattice models for conjugate A^(1)_n. J. Phys. A 37 (2004) 29372947, hepth/0309068.
 (With P.R. Pinto). Modular invariants and the double of the Haagerup subfactor. Sinaia Proceedings, Modular invariants and the double of the Haagerup subfactor.. In Advances in Operator Algebras and Mathematical Physics. (Sinaia 2003, F.P. Boca, O. Bratteli, R. Longo, H. Siedentop eds.) pp. 6788, The Theta Foundation, Bucharest, 2006.
 Modular invariant partition functions in statistical mechanics, conformal field theory and their realisation by subfactors. Proceedings Congress of the International Association of Mathematical Physics, Lisbon 2003, editor JC Zambrini, pp 464475, World Scientific Press,Singapore 2005
 Twisted Ktheory and Modular Invariants: Quantum Doubles of Finite Groups. The Abel Symposium 2004, 117144, Abel Symp., 1, Springer, Berlin, 2006.
 From Ising to Haagerup, Markov Processes and Related Fields, Markov Processes and Related Fields, 13 (2007) 267287
 (With T. Gannon). Modular invariants and Twisted Equivariant Ktheory. Commun. Number Theory Phys., 3 (2009), 209296. arXiv:0807.3759
 (With M. Pugh). Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs. Münster J. Math., 2 (2009) 95142.. arXiv:0906.4307
 (With M. Pugh). SU(3)Goodmande la HarpeJones subfactors and the realisation of SU(3) modular invariants. Rev. Math. Phys., 21 (2009), no. 7, 877928. arXiv:0906.4252
 (With M. Pugh). A2Planar Algebras I, Quantum Topol. 1 (2010), 321377. arXiv:0906.4225 (math.OA)
 (With M. Pugh). A2Planar Algebras II: Planar Modules, J. Funct. Anal., to appear. arxiv:0906.4311 (math.OA)
 (With M. Pugh). Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory. Commun. Math. Phys., 295 (2010) 363413. arXiv:0906.4314
 (With M. Pugh). Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3), Commun. Math. Phys. 301 (2011), 771809. arXiv:1002.2348[math.OA]
 (With T. Gannon). The exoticness and realisability of the HaagerupIzumi modular data. Commun. Math. Phys. to appear, arXiv:1006.1326[math.QA]
 (With M. Pugh). The Nakayama automorphism of the almost CalabiYau algebras associated to SU(3) modular invariants, Comm. Math. Phys., to appear. arXiv:1008.1003 (math.OA)
 (With T. Gannon). Modular invariants and Twisted Equivariant Ktheory II: Dynkin diagram symmetries. arXiv:1012.1634[math.KT]
 (With P.R. Pinto). Subfactor realisation of modular invariants II. Inter. J of Mathematics, to appear
 (With M. Pugh). Braided Subfactors, Spectral Measures, Planar algebras and CalabiYau algebras associated to SU(3) modular invariants. arXiv:1110.4547
 (With M. Pugh). On the homology of almost CalabiYau algebras associated to SU(3) modular invariants. arXiv:1111.3585
 (With T. Gannon). The search for the exotic  subfactors and conformal field theories.
Research
Book
Quantum Symmetries on Operator Algebras with Yasuyuki Kawahigashi published by Oxford University Press. Here are the Updates/Corrections to the volume and some reviews by:
Vaughan Jones  American Mathematical Society
Carl Winslow  Mathematical Reviews
W. Slowikowski  Zentralblatt
European Network: EUNCG
Research Responsibilities since 2000
Coorganiser with S.L.Woronowicz of session on Operator Algebras and Noncommutative Geometry, Congress of International Association of Math. Physics, London, July 2000.
Member of Scientific Organising Committee of workshop on Modular Invariance, ADE, Subfactors, and Geometry of Moduli Spaces, Kyoto, November 2000.
Member of the University of Warwick Mathematics Research Centre Steering Committee, 20002005.
Coordinator of EPSRC Network ABCKLM on Algebraic Geometry, Boundary Conformal Field Theory and Noncommutative Geometry, 20012004.
Coordinator of EU Network in Quantum SpacesNoncommutative Geometry, 20026.
Coorganiser of LMS regional meeting on Mathematical Physics, Gregynog, November 2002.
Chairman, Wales Institute of Mathematical and Computational Sciences Steering Committee 20022005.
Mathematical Physics Cluster Coordinator, Wales Institute of Mathematical and Computational Sciences, 20072011
Coordinator of EU Network in Noncommutative Geometry, 20072011.
Organiser of EU Research Training Network Focused Semester on Noncommutative Geometry and Physics, Feb  July 2010.
Organiser of LMS Spitalfields meeting on Noncommutative Geometry and Physics, Cardiff, May 2010.
Organiser of LMS regional meeting on Operator Algebras and Mathematical Physics, Cardiff, June 2010.
Organiser of first Frontiers Lecture of the Learned Society of Wales given by Dan Voiculescu, Cardiff, July 2010.
Organiser of Frontiers Lecture of the Learned Society of Wales given by Sir Michael Atiyah, Cardiff, January 2011.
Coorganizer, with Nigel Higson and Shahn Majid of Newton Institute  WIMCS meeting on Noncommutative Geometry, Cardiff April 2012.
Chairman of Scientific Committee of Oporto Meeting on Geometry and Physics, July 2012.
External Funding Since 2000
Royal SocietyNATO fellowship for Dr Sergey Neshveyev (Kharkov) 2001
EPSRC Senior Visiting Fellowship for Prof F. Radulescu (Iowa) 2000/03 GR/M87896
LMS Regional Meeting – Wales – 2002
EU TMR Network 20022006
EPSRC Senior Visiting Fellowship for Prof T. Gannon (Edmonton) 20042006 GR/580592/01
EU Research Training Network in Noncommutative Geometry EUNCG with partners Bucharest, CNRS, Copenhagen, Dublin, ESI Vienna, Leuven, Munster, Odense, Oslo and Rome
Major Conference Talks Since 2004
Workshop on Tensor Categories in Mathematics and Physics, Erwin Schrodinger Institute, Vienna, June 2004.
Clay Symposium on Ktheory and Noncommutative Geometry, Institut Henri Poincare, Center Emil Borel, Paris, July 2004.
CMS/AMSI Workshop on Geometry of generalised Dirac operators, Canberra, August 2004.
Abel Symposium on Operator Algebras, Oslo, September 2004.
Symposium honoring the memory of Gert K. Pedersen, Copenhagen, May 2005.
A Conference to honour the memory of the late J. T. Lewis, his contributions to mathematics and its applications, Dublin, June 2005.
International conference on Operator Algebras and their connections to Mathematical Physics, Settat, Morocco, NovemberDecember 2005.
Operator Algebras and Applications, University of Southern Denmark, Odense, April 2006.
21st International Conference on Operator Theory, Timisoara, JuneJuly 2006.
Brazilian Operator Algebras Meeting, Florianopolis, Brazil July 2006.
Operator Algebras, Operator Theory and Applications (WOAT 2006), International Summer School and Workshop, Lisbon, September 2006.
Topics on von Neumann Algebras, BIRS, Banff, September 2006.
Free Probability, Operator Spaces and von Neuman algebras, Sibiu, Romania 916 June 2007.
Workshop on Noncommutative Dynamics and Applications, Fields Institute, 1620 July 2007.
Workshop on Noncommutative Geometry, Copenhagen, 2529 February 2008.
UNCG Annual Meeting, Dublin, 1620 June 2008.
Operator Algebras and Conformal Field Theory, ESI Vienna, 819 September 2008.
KMS States and Noncommutative Geometry, PIMS, Victoria, Canada, 19 June  10 July 2009.
Algebraic QFT  the first 50 years, Gottingen, July 29  31, 2009.
Workshop on Algebraic and Topological Aspects of Dbranes, University of Wurzburg, Germany, December 17  18, 2009.
Combinatorial, Bialgebra, and Analytic Aspects ESI Programme on Bialgebras in Free Probability, Schrodinger Institute Vienna. February 2011
ISAAC 8th International Congress, Moscow, August 2011
Shanks Workshop on Von Neumann algebras and conformal field theory, October 2011
Operator Algebras and Applications ,Settat, Morocco, 15 November 2011
Conference on von Neumann Algebras and Related Topics RIMS, Kyoto University, Japan. January 2012
The Tenth Annual Spring Institute Noncommutative Geometry and Operator Algebras, Vanderbilt University, Nashville, Tennessee, USA, 410 May 2012
XXth Oporto Meeting on Geometry, Topology and Physics, Oporto University, Portugal, 1822 July 2012
The XXIX International Colloquium on GroupTheoretical Methods in Physics, Chern Institute of Mathematics, Tianjin, China, 2026 August 2012
Quantum Probabilistic Symmetries, 2012 LMS Regional Meeting and Workshop, Aberystwyth, 37 September 2012
Postgraduate Students
Graduated (Since 2000)
Dr Mathew Pugh, PhD 2009
Dr Gwion Evans, PhD 2003
Dr Paulo Rocha Pinto, PhD 2003
Dr Michael J. Gabriel, PhD 2000
Search the Mathematics Genealogy Project
Current Students
Ms. Claire Shelly
Biography
BA with first class honours: Oxford 1972
Msc: Oxford 1973
DPhil: Oxford 1975
Prizes
University of Oxford:
Junior Mathematical Prize, 1972
Senior Mathematical and Johnson Prizes, 1975
London Mathematical Society:
Whitehead Prize 1989
Fellowship
Elected Fellow of the Learned Society of Wales in the Inaugural Election 2010  2011
Appointments
Positions Held
October 1975  August 1976. Research Scholar at the School of Theoretical Physics, Dublin Institute for Advanced Studies, Ireland.
August 1976  August 1977. Research Assistant at the Institute of Mathematics, University of Oslo, Norway.
September 1977  December 1977. Visiting Assistant Professor at the Department of Mathematics, UCLA, Los
Angeles, California, USA.
January 1978  January 1979. Research Fellow of the Royal Society, under the European Exchange Programme, at the Institute of Mathematics, University of Copenhagen,Denmark.
January 1979  March 1979. Visiting Postdoctoral Research Fellow at the Department of Mathematics, University of Ottawa, Ottawa, Ontario, Canada.
April 1979  December 1979. SRC Research Fellow at the School of Mathematics, University of NewcastleuponTyne.
January 1980  September 1986. Lecturer in Mathematics at the University of Warwick.
October 1986  September 1987. Reader in Mathematics at the University of Warwick.
September 1987  April 1998. Professor in Mathematics, University of Wales, Swansea.
May 1998  to date. Professor in Mathematics, University of Wales, Cardiff.
September 2007  to date. Research Professor in the Wales Institute of Mathematical and Computational Sciences
Visiting Positions
October 1979  December 1979. Visitor to Sonderforschungsbereich 123, (Stochastische Mathematische Modelle), at the University of Heidelberg, Germany.
August 1982  December 1982. Visiting Fellow at the Department of Mathematics, Institute for Advanced Studies, Australian National University, Canberra, Australia.
December 1982  April 1983. Guest Scholar at Research Institute for Mathematical Sciences, Kyoto University, Japan. Supported by the Royal Society.
June 1983  August 1983. Research Fellow, Department of Mathematics, University of Ottawa, Canada.
July 1985  September 1985. Guest Scholar at Research Institute for Mathematical Sciences, Kyoto University, Japan. Supported by SERC.
February 1989  May 1989. Invited member, MittagLeffler Institute, Stockholm, Sweden.
July 1989  September 1989. Visiting Fellow at the Centre for Mathematical Analysis, Australian National University, Canberra, Australia.
September 1990  May 1991. Guest Professor at Research Institute for Mathematical Sciences, Kyoto University, Japan.
February 1999  April 1999. Visiting Fellow at the Centre for Mathematics and Applications, Australian National University, Canberra, Australia.