# Professor David E Evans

Honorary Distinguished Professor

- evansde@caerdydd.ac.uk
- M/2.39, 2nd Floor, Mathematics Institute, Senghennydd Road, Cardiff, CF24 4AG

- Welsh speaking

## Overview

### Research interests

I work in operator algebras and applications and connections with K-theory, dynamical systems, statistical mechanics and conformal quantum field theory.

### Administrative duties

- Golygydd Gwerddon Editor

## Biography

### Education

- 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 198. 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, Cardiff University
- 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 - April 1999. Visiting Fellow at the Centre for Mathematics and Applications, Australian National University, Canberra, Australia.
- January - June 2017. Lead Organizer, Operator Algebras: Subfactors and Applications, Isaac Newton Institute, Cambridge University
- Septembrer - October 2019 JSPS Invitational Fellow, Kyoto University
- February - May 2020 Research Professor MSRI Berkely

## Publications

### 2021

- Evans, D. E. and Pugh, M. 2021. Classification of module categories for SO(3)_{2m}. Advances in Mathematics 384, article number: 107713. (10.1016/j.aim.2021.107713)

### 2020

- Aaserud, A. N. and Evans, D. E. 2020. Realizing the braided Temperley-Lieb-Jones C*-tensor categories as Hilbert C*-modules. Communications in Mathematical Physics 380, pp. 103-130. (10.1007/s00220-020-03729-w)
- Evans, D. E. and Pugh, M. J. 2020. Spectral measures for G2 II: finite subgroups. Reviews in Mathematical Physics 32(8), article number: 2050026. (10.1142/S0129055X20500269)
- Aaserud, A. and Evans, D. 2020. K-theory of AF-algebras from braided C*-tensor categories. Reviews in Mathematical Physics 32(8), article number: 2030005. (10.1142/S0129055X20300058)
- Bratteli, T.et al. 2020. Ola Bratteli and his diagrams. Notices of the American Mathematical Society 67(5), pp. 665-675. (10.1090/noti2085)
- Evans, D. E. and Gannon, T. 2020. Tambara-Yamagami, loop groups, bundles and KK-theory. arXiv

### 2018

- Evans, D. and Gannon, T. 2018. Reconstruction and local extensions for twisted group doubles, and permutation orbifolds. arXiv

### 2017

- Evans, D. E. and Gannon, T. 2017. Non-unitary fusion categories and their doubles via endomorphisms. Advances in Mathematics 310, pp. 1-43. (10.1016/j.aim.2017.01.015)

### 2016

- Evans, D. E. and Pugh, M. . 2016. Spectral measures associated to rank two Lie groups and finite subgroups of GL(2,Z). Communications in Mathematical Physics 343, pp. 811-850. (10.1007/s00220-015-2434-5)

### 2015

- Evans, D. E. and Pugh, M. 2015. Spectral measures for G2. Communications in Mathematical Physics 337, pp. 1161-1197. (10.1007/s00220-015-2293-0)
- Evans, D. E. and Pugh, M. 2015. Spectral measures for Sp(2). arXiv, article number: 1404.1912.v2.
- Evans, D. 2015. Subfactors, twisted equivariant K-theory and conformal field theory.. Presented at: Subfactors and Conformal Field Theory, MFO Oberwolfach, 22-28 March 2015 Presented at Bisch, D. et al. eds.Oberwolfach Reports, Vol. 12. Mathematisches Forschungsinstitut Oberwolfach: pp. 849-926., (10.14760/OWR-2015-16)

### 2014

- Evans, D. E. and Gannon, T. 2014. Near-group fusion categories and their doubles. Advances in Mathematics 255, pp. 586-640. (10.1016/j.aim.2013.12.014)

### 2013

- Evans, D. E. and Gannon, T. 2013. Modular invariants and twisted equivariant K-theory II: Dynkin diagram symmetries. Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology 12(2), pp. 273-330. (10.1017/is013003008jkt221)
- Evans, D. E. and Pugh, M. J. 2013. Braided subfactors, spectral measures, planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants. Presented at: EU - NCG 4: EU - NCG 4th Annual Meeting, Bucharest, Romania, 25-30 April 2011 Presented at Popescu, I. and Purice, R. eds.Progress in Operator Algebras, Noncommutative Geometry, and their Applications: Proceedings of the 4th Annual Meeting of the European Noncommutative Geometry Network. pp. 17-60.

### 2012

- Evans, D. E. and Pugh, M. J. 2012. The Nakayama Automorphism of the almost Calabi-Yau Algebras associated to SU(3) modular invariants. Communications in Mathematical Physics 312(1), pp. 179-222. (10.1007/s00220-011-1389-4)
- Evans, D. E. and Pugh, M. J. 2012. On the homology of almost Calabi-Yau algebras associated to su(3) modular invariants. Journal of Algebra 368, pp. 92-125. (10.1016/j.jalgebra.2012.06.011)
- Evans, D. E. and Pinto, P. 2012. Subfactor realization of modular invariants: II. International Journal of Mathematics 23(3), article number: 1250030. (10.1142/S0129167X12500309)
- Evans, D. E. and Gannon, T. 2012. The search for the exotic - subfactors and conformal field theories. Presented at: ISAAC 2011 - 8th International Congress, Moscow, Russia, 22-27 August 2011 Presented at Burenkov, V. I. et al. eds.Progress in Analysis". Proceedings of the 8th Congress of the International Society for Analysis, its Applications, and Computation (22-27 August 2011), Vol. 1. Moscow: Moscow Peoples' Friendship University of Russia pp. 8-25.

### 2011

- Evans, D. E. and Pugh, M. J. 2011. A(2)-planar algebras II: Planar modules. Journal of Functional Analysis 261(7), pp. 1923-1954. (10.1016/j.jfa.2011.05.023)
- Evans, D. E. and Pugh, M. J. 2011. Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3). Communications in Mathematical Physics 301(3), pp. 771-809. (10.1007/s00220-010-1157-x)
- Evans, D. E. and Gannon, T. 2011. The exoticness and realisability of twisted Haagerup-Izumi modular data. Communications in Mathematical Physics 307(2), pp. 463-512. (10.1007/s00220-011-1329-3)

### 2010

- Evans, D. E. and Pugh, M. J. 2010. Spectral measures and generating series for Nimrep graphs in subfactor theory. Communications in Mathematical Physics 295(2), pp. 363-413. (10.1007/s00220-009-0902-5)
- Evans, D. E. and Pugh, M. J. 2010. A2-planar algebras I. Quantum Topology 1(4), pp. 321-377. (10.4171/QT/8)

### 2009

- Evans, D. E. and Pugh, M. J. 2009. SU(3)-Goodman-De La Harpe-Jones Subfactors and the Realization of SU(3) Modular Invariants. Reviews in Mathematical Physics 21(7), pp. 877-928. (10.1142/S0129055X09003761)
- Evans, D. E. and Pugh, M. J. 2009. Ocneanu cells and Boltzmann weights for the SU(3) ADE graphs. Munster Journal of Mathematics 2, pp. 94-142.
- Evans, D. E. and Gannon, T. 2009. Modular invariants and twisted equivariant K-theory. Communications in Number Theory and Physics 3(2), pp. 209-296. (10.4310/CNTP.2009.v3.n2.a1)

### 2007

- Evans, D. E. 2007. From Ising to Haagerup. Markov Processes and Related Fields 13(2), pp. 267-287.

### 2006

- Evans, D. E. 2006. Twisted K-theory and modular invariants: I Quantum doubles of finite groups. Presented at: Proceedings of the First Abel Symposium, Oslo, Norway.
- Tucker, J. V. and Evans, D. E. 2006. Science Academy - the case for a new Welsh Academy. The Welsh Agenda, Institute for Welsh Affairs Summer, pp. 37-38.

### 2005

- Evans, D. E. 2005. Modular invariant partition functions in statistical mechanics, conformal field theory and their realisation by subfactors. Presented at: XIVth International Congress on Mathematical Physics, Lisbon, Portugal, 28 July – 2 August 2003 Presented at Zambrini, J. C. ed.XIVth International Congress on Mathematical Physics. Hackensack, NJ: World Scientific Publishing pp. 464-475., (10.1142/9789812704016_0045)

### 2004

- Behrend, R. E. and Evans, D. E. 2004. Integrable lattice models for conjugate An(1). Journal of Physics A Mathematical and General 37(8), pp. 2937-2947. (10.1088/0305-4470/37/8/006)

### 2003

- Evans, D. E. and Pinto, P. R. 2003. Subfactor realisation of modular invariants. Communications in mathematical physics 237(1-2), pp. 309-363. (10.1007/s00220-003-0862-0)
- Evans, D. E. 2003. Critical phenomena, modular invariants and operator algebras. Presented at: Operator Algebras and Mathematical Physics, Constanta, Romania, July 2001 Presented at Combes, J. M. et al. eds.Operator algebras and mathematical physics. Bucharest: Theta Foundation pp. 89-113.

### 2002

- Evans, D. E. 2002. Fusion rules of modular invariants. Reviews in Mathematical Physics 14(7 & 8), pp. 709-731. (10.1142/S0129055X02001351)

### 2001

- Böckenhauer, J. M., Evans, D. E. and Kawahigashi, Y. 2001. Longo-Rehren subfactors arising from alpha-induction. Publications of the Research Institute for Mathematical Sciences Kyoto University 37(1), pp. 1-35. (10.2977/prims/1145476688)

### 2000

- Böckenhauer, J. and Evans, D. E. 2000. Modular invariants from subfactors: type I coupling matrices and intermediate subfactors. Communications in Mathematical Physics 213(2), pp. 267-289. (10.1007/s002200000241)
- Böckenhauer, J., Evans, D. E. and Kawahigashi, Y. 2000. Chiral structure of modular invariants for subfactors. Communications in Mathematical Physics 210(3), pp. 733-784. (10.1007/s002200050798)
- Bratteli, O., Evans, D. E. and Jorgensen, P. E. 2000. Compactly supported wavelets and representations of the Cuntz relations. Applied and Computational Harmonic Analysis 8(2), pp. 166-196. (10.1006/acha.2000.0283)
- Böckenhauer, J. and Evans, D. E. 2000. Modular invariants from subfactors. Contemporary Mathematics, pp. 95-131.
- Boeckenhauer, J. and Evans, D. E. 2000. Modular invariants and subfactors. Fields Institute Communications 30, pp. 11-37.

### 1999

- Böckenhauer, J. and Evans, D. E. 1999. Modular invariants, graphs and α-induction for nets of subfactors. II. Communications in Mathematical Physics 200(1), pp. 57-103. (10.1007/s002200050523)
- Böckenhauer, J., Evans, D. E. and Kawahigashi, Y. 1999. On α-induction, chiral generators and modular invariants for subfactors. Communications in Mathematical Physics 208(2), pp. 429-487. (10.1007/s002200050765)
- Böckenhauer, J. and Evans, D. E. 1999. Modular invariants, graphs and α-Induction for nets of subfactors. III. Communications in Mathematical Physics 205(1), pp. 183-228. (10.1007/s002200050673)

### 1998

- Bratteli, O.et al. 1998. Homotopy of a pair of approximately commuting unitaries in a simple C*-algebra. Journal of Functional Analysis 160(2), pp. 466-523. (10.1006/jfan.1998.3261)
- Elliott, G., Evans, D. E. and Kishimoto, A. 1998. Outer conjugacy classes of trace scaling automorphisms of stable UHF algebras. Mathematica Scandinavica 83, pp. 74-86.
- Evans, D. E. and Kawahigashi, Y. 1998. Orbifold subfactors from Hecke algebras II - Quantum doubles and braiding. Communications in Mathematical Physics 196(2), pp. 331-361. (10.1007/s002200050424)
- Böckenhauer, J. and Evans, D. E. 1998. Modular invariants, graphs and a-induction for nets of subfactors I. Communications in Mathematical Physics 197(2), pp. 361-386. (10.1007/s002200050455)
- Evans, D. E. and Kawahigashi, Y. 1998. Quantum symmetries on operator algebras. Oxford Mathematical Monographs. Oxford: Oxford University Press.

### 1997

- Evans, D. E. and Kishimoto, A. 1997. Trace scaling automorphisms of certain stable AF algebra. Hokkaido Journal of Mathematics 26(1), pp. 211-224.

### 1995

- Bratteli, O., Evans, D. E. and Kishimoto, A. 1995. The Rohlin property for quasi-free automorphisms of the Fermion algebra. Proceedings of the London Mathematical Society s3-71(3), pp. 675-694. (10.1112/plms/s3-71.3.675)

### 1994

- Evans, D. E. and Kawahigashi, Y. 1994. Orbifold subfactors from Hecke algebras. Communications in Mathematical Physics 165(3), pp. 445-484. (10.1007/BF02099420)
- Bratteli, O.et al. 1994. Finite group actions on AF algebras obtained by folding the interval. K-Theory 8(5), pp. 443-464. (10.1007/BF00961400)
- Evans, D. E. and Kawahigashi, Y. 1994. The E7 commuting squares produce D10 as principal graph. Publications of the Research Institute for Mathematical Sciences 30(1), pp. 151-166. (10.2977/prims/1195166280)

### 1993

- Bratteli, O., Evans, D. E. and Kishimoto, A. 1993. Crossed products of totally disconnected spaces by. Ergodic Theory and Dynamical Systems 13(3), pp. 445-484. (10.1017/S0143385700007483)
- Elliott, G. and Evans, D. E. 1993. The structure of the irrational rotation C*-algebra. Annals of Mathematics 138(3), pp. 477-501.

### 1992

- Bratteli, O.et al. 1992. Non-commutative spheres II: rational rotations. Journal of Operator Theory 27(1), pp. 53-85.

### 1991

- Evans, D. E. and Kishimoto, A. 1991. Compact group actions on UHF algebras obtained by folding the interval. Journal of Functional Analysis 98(2), pp. 346-360. (10.1016/0022-1236(91)90082-G)
- Beggs, E. J. and Evans, D. E. 1991. The real rank of algebras of matrix valued functions. International Journal of Mathematics, pp. 131-138.
- Bratteli, O.et al. 1991. Non-commutative spheres I. International Journal of Mathematics 2(2), pp. 139-166. (10.1142/S0129167X91000090)

### 1989

- Connes, A. and Evans, D. E. 1989. Embeddings of U(1)-current algebras in non-commutative algebras of classical statistical mechanics. Communications in Mathematical Physics 121(3), pp. 507-525. (10.1007/BF01217736)
- Bratteli, O.et al. 1989. Quasi-product actions of a compact abelian group on a C* algebra. Tohoku Mathematical Journal 41(1), pp. 133-161. (10.2748/tmj/1178227871)

### 1988

- Evans, D. E. and Kishimoto, A. 1988. Duality for automorphisms on a compact C*-dynamical system. Ergodic Theory and Dynamical Systems 8(2), pp. 173-189. (10.1017/S0143385700004405)
- Evans, D. E. and Carey, A. L. 1988. The operator algebras of the two dimensional Ising model. Presented at: Braids, Santa Cruz, CA, USA, August 1987.

### 1986

- Bratteli, O., Elliott, G. and Evans, D. E. 1986. Locality and differential operators on C*-algebras. Journal of Differential Equations 64(2), pp. 221-273. (10.1016/0022-0396(86)90088-4)
- Evans, D. E. and Lewis, J. T. 1986. On a C*-algebra approach to phase transition in the two-dimensional Ising model. II. Communications in Mathematical Physics 102(4), pp. 521-535. (10.1007/BF01221645)

### 1984

- Araki, H., Carey, A. and Evans, D. E. 1984. On O_{n+1}. Journal of Operator Theory 12(2), pp. 247-264.

### 1983

- Araki, H. and Evans, D. E. 1983. On a C*-algebra approach to phase transition in the two-dimensional Ising model. Communications in Mathematical Physics 91(4), pp. 489-503. (10.1007/BF01206017)
- Bratteli, O. and Evans, D. E. 1983. Dynamical semigroups commuting with compact abelian actions. Ergodic Theory and Dynamical Systems 3(2), pp. 187-217. (10.1017/S0143385700001929)

### 1980

- Evans, D. E. 1980. A review on semigroups of completely positive maps. Presented at: Congress of the International Association of Mathematical Physics, Lausanne, Switzerland, August 1979Proceeding of Conference of International Assoc. of Math. Physics. pp. 400-406.

### 1979

- Christensen, E. and Evans, D. E. 1979. Cohomology of operator algebras and quantum dynamical semigroups. Journal of the London Mathematical Society s2-20(2), pp. 358-368. (10.1112/jlms/s2-20.2.358)
- Evans, D. E. and Hanche-Olsen, H. 1979. The generators of positive semigroups. Journal of Functional Analysis 32(2), pp. 207-212. (10.1016/0022-1236(79)90054-5)

### 1977

- Evans, D. E. and Lewis, J. T. 1977. Dilations of Irreversible Evolutions in Algebraic Quantum Theory. Communications of the Dublin Institute for Advanced Studies, Series A: Theoretical Physics Vol. 24. Dublin: Dublin Institute for Advanced Studies.

### 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

- MathsSciNet (Please be aware that MathSciNet searching is only possible if you are accessing this page from an institution with a MathSciNet subscription.)
- Google Scholar Profile
- My ArVix Papers

### Video Talks

- Subfactors and Algebraic Aspects of Quantum Field Theory, MSRI Berkeley December 2000

Video: Modular invariants from Subfactors - Algebraic Quantum Field Theory – the first 50 Years, Gottingen July 2009

Video: Operator Algebras: Impact of AQFT on Subfactors and K-theory - Shanks Workshop "Conformal Field Theory and Von Neumann Algebras, Vanderbilt, October 2011.

Video: The search for the exotic - subfactors and conformal field theories - Subfactors and Fusion Categories, BIRS, Banff, April 2014

Video: Quantum Doubles of Quadratic Systems I

### Books

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

### 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, Cardiff, July 2010 by Dan Voiculescu and subsequent lectures by Sir Michael Atiyah (2011), Alain Connes and Lyn Evans (2012), Sir Vaughan Jones (2013)
- Co-organizer, with Nigel Higson and Shahn Majid of Newton Institute - WIMCS meeting on Noncommutative Geometry, Cardiff April 2012
- Chairman of Scientific Committee of XXth Oporto Meeting on Geometry and Physics, July 2012
- Member of Scientific Organizing Committee, Workshop on Gauge Theory and Noncommutative Geometry, June 2012, Luxembourg
- Member of Scientific Advisory Committee of LMS Regional Meeting and Workshop on Quantum Probabilistic Symmetries, Aberystwyth, September 2012
- Reviewer for Romanian National Council for Scientific Research for 2012 National Call
- Member of Appointments Panel for Accenture Associate Professorship in Mathematics, Trinity College Dublin 2013
- Member of Scrutiny Committee for Mathematics, Computer Science and Statistics for the Learned Society of Wales 2011-13
- Member of the Council of the Learned Society of Wales, 2014-17.
- Lead organiser of Newton Institute Programme on Operator Algebras: Subfactors and Applications, January-June 2017.

### 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
- LMS Visit of V Manuilov, December 2003
- 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
- EPSRC ABC-KLM Network in Algebraic Geometry, Boundary Conformal Field Theory and Noncommutative Geometry. GR/R36596/01
- LMS Collaborative Award Scheme 3 with Aberystwyth and Swansea, 2008-09
- LMS Spitalfields Meeting, 2010
- LMS Regional Meeting and Workshop, 2010
- EPSRC award on The Haagerup subfactor, K-theory and conformal field theory, 2012-15 EP/J003352/1
- EPSRC 2016-19 EP/N022432/1

### 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
- EU-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
- Programme on K-theory and Quantum Fields, Erwin Schrodinger Institute, Vienna, July 2012
- The XXIX International Colloquium on Group-Theoretical Methods in Physics, Chern Institute of Mathematics, Tianjin, China, 20-26 August 2012
- Heilbronn Day: Modular forms, geometry and physics, ICMS Edinburgh, 23 November 2012
- COSy 2013 - Canadian Symposium on Operator Algebras and Their Applications, Fields Institute, Toronto, Canada, 27-31 May 2013
- Subfactors in Maui 2013, Hawaii, 15-19 July 2013
- Classifying Structures for Operator Algebras and Dynamical Systems, Aberystwyth, Wales, 16-20 September 2013
- C*-algebras in Scotland, Aberdeen, Scotland, 26 October 2013
- Graduate Student Meeting, LMS 15 November 2013, slides and more orbifolds
- Subfactors and Fusion Categories, BIRS Banff 13-18 April 2014
- NCGOA14, Subfactors, Conformal Field Theory and Vertex Operator Algebras, Vanderbilt USA, 2-8 May 2014
- Subfactor Theory in Mathematics and Physics, Maui, Hawaii, 14-18 July 2014
- Subfactors and Conformal Field Theory, Oberwolfach, 22-28 March 2015
- Erikfest: Conference on Operator Algebras and Applications, Copenhagen, 4-8 May 2015
- Lie Groups, Lie Algebras and their Representations, University of Alberta, Edmonton, Canada, 16-17 May , 2015
- George Boole Mathematical Sciences Conference, Cork, Ireland, 17-28 August 2015
- Kansai Operator Algebra Seminar, Kinosaki, Japan, 12-13 December 2015
- MSJ-SI Operator Algebras and Mathematical Physics,Tohoku University, Japan, 1-12 August 2016
- Danish-Norwegian Workshop on Operator Algebras, Lysebu, Oslo, 5-8 January 2017
- Advances in Mathematics and Theoretical Physics, Palazzo Corsini, Accademia dei Lincei, Rome, 19-22 September 2017
- Current Progress in Mathematical Physics, Harvard, 10-12 December 2018
- Mathematics of interacting QFT models, York, 1-5 July 2019