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Professor David E Evans

Overview

person name Position: Research Professor of Mathematics Email: EvansDE@cardiff.ac.uk
 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 two-dimensional 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 K-theory – 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 K-theory. Commun. Number Theory Phys., 3 (2009), 209-296. arXiv:0807.3759[math.KT]

(With M. Pugh). Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory. Commun. Math. Phys., 295 (2010) 363-413. arXiv:0906.4314[math.OA]

(With T. Gannon). The exoticness and realisability of the Haagerup-Izumi modular data. Commun. Math. Phys., to appear. arXiv:1006.1326[math.QA]

(With T. Gannon). Modular invariants and Twisted Equivariant K-theory 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 – EU-NCNG

Operator Algebras Seminar Organiser

Coordinator of EPSRC Network - ABC-KLM

Wales Mathematics Video Seminars

WIMCS Mathematical Physics Cluster Manager

Member of WIMCS Research Committee

Personal Website

Professor David E Evans' Personal Website

Publications

  • MathsSciNet

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Video Talks

Algebraic Quantum Field Theory – the first 50 Years, Gottingen July 2009
Operator Algebras: Impact of AQFT on Subfactors and K-theory

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) 11-72.
  • (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) 466-523.
  • (With G.A. Elliott, A. Kishimoto). Outer conjugacy classes of trace scaling automorphisms of stable UHF algebras. Math. Scand. 83 (1998) 74-86.
  • (With A. Kishimoto). Trace scaling automorphisms of certain stable AF algebras. Hokkaido Math. J., 26 (1997), 211-224.
  • (With Y. Kawahigashi). Orbifold subfactors from Hecke algebras II: quantum double and braiding. Commun. Math. Phys. 196 (1998) 331-361, funct-an/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), 123-135, 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) 166-196.
  • (With J.Boeckenhauer). Modular invariants, graphs and alpha-induction for nets of subfactors I. Commun. Math. Phys. 197 (1998) 361-386, hep-th/9801171.
  • (With J.Boeckenhauer). Modular invariants, graphs and alpha-induction for nets of subfactors II. Commun. Math. Phys. 200 (1999) 57-103, hep-th/98005023.
  • (With J.Boeckenhauer). Modular Invariants, graphs and alpha-induction for Nets of Subfactors III. Commun. Math. Phys. 205 (1999) 183-228, hep-th/9812110.
  • (With J.Boeckenhauer, Y. Kawahigashi). On alpha-induction, chiral projectors, and modular invariants for subfactors. Commun. Math. Phys. 208 (1999) 429-487, math.OA/9904109
  • (With J.Boeckenhauer, Y. Kawahigashi). Chiral structure of modular invariants for subfactors. Commun. Math. Phys. 210 (2000) 733-784, math.OA/9907149.
  • (With J.Boeckenhauer, Y. Kawahigashi). Longo-Rehren subfactors arising from alpha-induction. Publ. RIMS Kyoto37 (2001) 1-35, math.OA/0002154.
  • (With J.Boeckenhauer). Modular invariants from subfactors: Type I coupling matrices and intermediate subfactors. Commun. Math. Phys. 213 (2000) 267-289, math.OA/9911239.
  • (With J.Boeckenhauer). Modular invariants from subfactors. In Quantum Symmetries in Theoretical Physics and Mathematics (Bariloche, 2000), 95-131, 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), 11-37, Fields Inst. Commun., 30, Amer. Math. Soc., Providence, RI, 2001, math.OA/0008056.
  • From XY to ADE. In Geometric analysis and applications (Canberra, 2000), 85-105, Proc. Centre Math. Appl. Austral. Nat. Univ., 39, Austral. Nat. Univ., Canberra, 2001.
  • Fusion rules of modular invariants. Reviews in Math. Physics, 14 (2002) 709-732, 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) 119-130, Providence, RI, Amer. Math. Soc., math.OA/0309175.
  • (With P.R. Pinto). Subfactor realisation of modular invariants. Commun. Math. Phys. 237 (2003) 309-363, math.OA/0309174.
  • (With R. E. Behrend). Integrable lattice models for conjugate A^(1)_n. J. Phys. A 37 (2004) 2937-2947, hep-th/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. 67-88, 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 J-C Zambrini, pp 464--475, World Scientific Press,Singapore 2005
  • Twisted K-theory and Modular Invariants: Quantum Doubles of Finite Groups. The Abel Symposium 2004, 117--144, Abel Symp., 1, Springer, Berlin, 2006.
  • From Ising to Haagerup, Markov Processes and Related Fields, Markov Processes and Related Fields, 13 (2007) 267-287
  • (With T. Gannon).  Modular invariants and Twisted Equivariant K-theory. Commun. Number Theory Phys., 3 (2009), 209-296. arXiv:0807.3759
  • (With M. Pugh). Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs. Münster J. Math., 2 (2009) 95-142.. arXiv:0906.4307
  • (With M. Pugh). SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants. Rev. Math. Phys., 21 (2009), no. 7, 877-928. arXiv:0906.4252
  • (With M. Pugh). A2-Planar Algebras I, Quantum Topol. 1 (2010), 321-377. arXiv:0906.4225 (math.OA)
  • (With M. Pugh). A2-Planar 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) 363-413. 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), 771-809. arXiv:1002.2348[math.OA]
  • (With T. Gannon). The exoticness and realisability of the Haagerup-Izumi modular data. Commun. Math. Phys. to appear, arXiv:1006.1326[math.QA]
  • (With M. Pugh). The Nakayama automorphism of the almost Calabi-Yau 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 K-theory 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 Calabi-Yau algebras associated to SU(3) modular invariants. arXiv:1110.4547
  • (With M. Pugh). On the homology of almost Calabi-Yau 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

Palle Jorgensen - Amazon

European Network: EU-NCG

Research Responsibilities since 2000

Co-organiser with S.L.Woronowicz of session on Operator Algebras and Non-commutative 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, 2000-2005.

Coordinator of EPSRC Network ABC-KLM on Algebraic Geometry, Boundary Conformal Field Theory and Noncommutative Geometry, 2001-2004.

Coordinator of EU Network in Quantum Spaces-Noncommutative Geometry, 2002-6.

Co-organiser of LMS regional meeting on Mathematical Physics, Gregynog, November 2002.

Chairman, Wales Institute of Mathematical and Computational Sciences Steering Committee 2002-2005.

Mathematical Physics Cluster Coordinator, Wales Institute of Mathematical and Computational Sciences, 2007-2011

Co-ordinator of EU Network in Noncommutative Geometry, 2007-2011.

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.

Co-organizer, 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 Society-NATO 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 2002-2006

EPSRC Senior Visiting Fellowship for Prof T. Gannon (Edmonton) 2004-2006 GR/580592/01

EU Research Training Network in Noncommutative Geometry EU-NCG 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 K-theory and Non-commutative 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, November-December 2005.

Operator Algebras and Applications, University of Southern Denmark, Odense, April 2006.

21st International Conference on Operator Theory, Timisoara, June-July 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 9-16 June 2007.

Workshop on Noncommutative Dynamics and Applications, Fields Institute, 16-20 July 2007.

Workshop on Noncommutative Geometry, Copenhagen, 25-29 February 2008.

U-NCG Annual Meeting, Dublin, 16-20 June 2008.

Operator Algebras and Conformal Field Theory, ESI Vienna, 8-19 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 D-branes, 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, 1-5 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, 4-10 May 2012

XXth Oporto Meeting on Geometry, Topology and Physics, Oporto University, Portugal, 18-22 July 2012

The XXIX International Colloquium on Group-Theoretical Methods in Physics, Chern Institute of Mathematics, Tianjin, China, 20-26 August 2012

Quantum Probabilistic Symmetries, 2012 LMS Regional Meeting and Workshop, Aberystwyth, 3-7  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 Newcastle-upon-Tyne.

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, Mittag-Leffler 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.