Operator algebras: subfactors and their applications
OAS
9 January 2017 to 23 June 2017
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Programme theme
The study of subfactors was initiated by Vaughan Jones in the early 1980's, in the theory of von Neumann algebras of operators on Hilbert spaces. Subfactor theory rapidly led to connections with link and 3-manifold invariants, quantum groups and exactly solvable models in statistical mechanics reinforcing the connections with physics. Subsequently deep applications and connections have been uncovered with algebraic, topological and conformal quantum field theory, with rapid progress in recent years in these applications. Free probability and planar algebra techniques have been combined to not only construct subfactors but derive matrix model computations in loop models of statistical mechanics.
These developments have led to connections between subfactors, non-commutative geometry and conformal field theory. In particular relationships between conformal nets of factors, twisted equivariant K-theory, K-homology, KK-theory, fusion and module categories and vertex operator algebras. The K-theoretic aspect of the programme includes higher twists as higher Dixmier-Douady twists and the categorification or higher geometry fronts. The search for geometric description of elliptic cohomology has led to relations with conformal field theories and conformal nets.
The programme will focus on these wide ranging applications as well as the underlying structure theory of operator algebras and subfactors. The classification of subfactors of small index has made strides in the last few years, involving the newer planar algebra tools, including the complete classification of subfactors with index values in the interval [4,5] and significant progress between 5 to just beyond 6. However there are very few constructions of subfactors that do not rely on group or quantum group symmetries. The challenge is to understand and even construct these allegedly exotic subfactors in a natural way and realising modular tensor categories as conformal field theories with conformal nets of factors and vertex operator algebras. There is much recent evidence that the Haagerup subfactor for example yields a natural conformal field theory.
Click here to download the programme's final scientific report
Preprints
| Title | Year | Programme |
|---|---|---|
Operator algebras for higher rank analysis and their application to factorial languagesAuthors: Adam Dor-On, Evgenios Kakariadis |
2016 | OAS |
Yang-Baxter representations of the infinite symmetric groupAuthors: Ulrich Pennig, Simon Wood, Gandalf Lechner |
2016 | OAS |
Free multivariate semicrossed products: reflexivity and the bicommutant propertyAuthors: Robert T. Bickerton, Evgenios Kakariadis |
2016 | OAS |
On the quantized dynamics of factorial languagesAuthors: Evgenios Kakariadis, Christopher Barrett |
2016 | OAS |
Yoh TanimotoAuthors: Roberto Longo, Yoshimichi Ueda, Yoh Tanimoto |
2016 | OAS |
Bernoulli actions of type III_1 and L^2-cohomologyAuthors: Jonas Wahl, Stefaan Vaes |
2016 | OAS |
Euler totient of subfactor planar algebrasAuthors: Sebastien Palcoux |
2016 | OAS |
Non-semisimple planar algebras from the representation theory of ${\overline{U}_q}{(\mathfrak{sl}_2)}$Authors: Stephen Moore |
2016 | OAS |
L^2-Betti numbers of rigid C*-tensor categories and discrete quantum groupsAuthors: David Kyed, Sven Raum, Matthias Valvekens, Stefaan Vaes |
2016 | OAS |
Workshops
Primer on subfactors and applications
11 January 2017 to 20 January 2017
Structure of operator algebras: subfactors and fusion categories
23 January 2017 to 27 January 2017
Subfactors, higher geometry, higher twists and almost Calabi-Yau algebras
27 March 2017 to 31 March 2017
Subfactors, K-theory and conformal field theory
12 June 2017 to 16 June 2017
OAS Follow on: Operator Algebras: Subfactors and Applications
26 June 2023 to 30 June 2023
Seminars
| Tuesday 31st January 2017 | |||
|---|---|---|---|
| 15:30 to 16:30 |
Scott Morrison Australian National University |
Room 1 | |
| Tuesday 7th February 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Yoh Tanimoto Università degli Studi di Roma Tor Vergata |
Room 2 | 
|
| Thursday 9th February 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Vincenzo Morinelli Università degli Studi di Roma Tor Vergata |
Room 2 |
|
| Tuesday 14th February 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Masaki Izumi Kyoto University |
Room 2 |
|
| Thursday 16th February 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Stefano Rossi Università degli Studi di Roma Tor Vergata |
Room 2 |
|
| Tuesday 21st February 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Denjoe O'Connor Dublin Institute for Advanced Studies |
Room 2 |
|
| Thursday 23rd February 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Ivan Todorov Queen's University Belfast |
Room 2 |
|
| Tuesday 28th February 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Evgenios Kakariadis University of Newcastle upon Tyne |
Room 2 |
|
| Thursday 2nd March 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Stephen Moore Cardiff University |
Room 2 | |
| Tuesday 7th March 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Keith Hannabuss University of Oxford |
Room 2 |
|
| Thursday 9th March 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Andreas Aaserud Cardiff University |
Room 2 |
|
| Tuesday 14th March 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Paul Fendley University of Oxford |
Room 2 |
|
| Thursday 16th March 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Makoto Yamashita Ochanomizu University |
Room 2 |
|
| Tuesday 21st March 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Yasu Kawahigashi University of Tokyo |
Room 2 |
|
| Thursday 6th April 2017 | |||
|---|---|---|---|
| 13:00 to 14:00 |
Valeriano Aiello Università degli Studi Roma Tre |
Room 2 | |
| Tuesday 11th April 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Kenny De Commer Vrije Universiteit Brussel |
Room 2 |
|
| Tuesday 18th April 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Yuki Arano Kyoto University |
Room 2 |
|
| Thursday 20th April 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Andrew McKee Queen's University Belfast |
Room 2 |
|
| Tuesday 25th April 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Yuki Arano Kyoto University |
Room 2 |
|
| Thursday 27th April 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Ingo Runkel King's College London |
Room 2 |
|
| Tuesday 2nd May 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Yuki Arano Kyoto University |
Room 2 |
|
| Thursday 4th May 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Roland Vergnioux Université de Caen Basse-Normandie |
Room 2 |
|
| Tuesday 9th May 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Yuki Arano Kyoto University |
Room 2 |
|
| Tuesday 16th May 2017 | |||
|---|---|---|---|
| 12:45 to 13:45 |
Dorothea Bahns Georg-August-Universität Göttingen |
Room 2 | |
| 14:00 to 15:00 |
Hans Wenzl University of California, San Diego |
Room 2 |
|
| Thursday 18th May 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
David Kyed University of Southern Denmark |
Room 2 |
|
| Tuesday 23rd May 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Ying-Fen Lin Queen's University Belfast |
Room 2 |
|
| Thursday 25th May 2017 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Jonathan Rosenberg University of Maryland, College Park |
Room 2 | |
| Friday 2nd June 2017 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Marius Dadarlat |
Room 2 |
|
| Tuesday 6th June 2017 | |||
|---|---|---|---|
| 12:45 to 13:45 |
Joachim Zacharias University of Glasgow |
Room 2 |
|
| 14:00 to 15:00 |
Marius Dadarlat |
Room 2 |
|
| Thursday 8th June 2017 | |||
|---|---|---|---|
| 12:45 to 13:45 |
Emmanuel Germain Université de Caen Basse-Normandie |
Room 2 |
|
| 14:00 to 15:00 |
Marius Dadarlat |
Room 2 |
|
| Tuesday 20th June 2017 | |||
|---|---|---|---|
| 13:30 to 14:30 |
Sven Raum EPFL - Ecole Polytechnique Fédérale de Lausanne |
Room 2 |
|
| 16:00 to 17:00 |
Masaki Izumi Kyoto University |
Room 2 |
|
Organisers
- David Evans Cardiff University
- Masaki Izumi Kyoto University
- Vaughan Jones Vanderbilt University; University of California, Berkeley
Speakers
- Andreas Aaserud Cardiff University
- Valeriano Aiello Università degli Studi Roma Tre
- Yuki Arano Kyoto University
- Dorothea Bahns Georg-August-Universität Göttingen
- Marius Dadarlat
- Kenny De Commer Vrije Universiteit Brussel
- Paul Fendley University of Oxford
- Emmanuel Germain Université de Caen Basse-Normandie
- Keith Hannabuss University of Oxford
- Masaki Izumi Kyoto University
- Evgenios Kakariadis University of Newcastle upon Tyne
- Yasu Kawahigashi University of Tokyo
- David Kyed Københavns Universitet (University of Copenhagen)
- Ying-Fen Lin Queen's University Belfast
- Andrew McKee Queen's University Belfast
- Stephen Moore Cardiff University
- Vincenzo Morinelli Università degli Studi di Roma Tor Vergata
- Scott Morrison Australian National University
- Denjoe O'Connor Dublin Institute for Advanced Studies
- Sven Raum EPFL - Ecole Polytechnique Fédérale de Lausanne
- Jonathan Rosenberg University of Maryland, College Park
- Stefano Rossi Università degli Studi di Roma Tor Vergata
- Ingo Runkel King's College London
- Yoh Tanimoto Università degli Studi di Roma Tor Vergata
- Ivan Todorov Queen's University Belfast
- Roland Vergnioux Université de Caen Basse-Normandie
- Hans Wenzl University of California, San Diego
- Makoto Yamashita Ochanomizu University
- Joachim Zacharias University of Glasgow
Participants
- Andreas Aaserud Cardiff University
- Valeriano Aiello Università degli Studi Roma Tre
- Yuki Arano Kyoto University
- Dorothea Bahns Georg-August-Universität Göttingen
- Edwin Beggs University of Wales, Swansea
- Henning Bostelmann University of York
- Jacek Brodzki University of Southampton
- Daniela Cadamuro Technischen Universität München
- Sayan Chakraborty Universität Münster
- Sandipan De Indian Statistical Institute, Bangalore; Institute of Mathematical Sciences, Chennai
- Kenny De Commer Vrije Universiteit Brussel
- Benjamin Doyon King's College London
- David Evans Cardiff University
- Paul Fendley University of Oxford
- Terry Gannon University of Alberta
- Emmanuel Germain Université de Caen Basse-Normandie
- Rolf Gohm Aberystwyth University
- Pinhas Grossman
- Iva Halacheva Lancaster University
- Amihay Hanany Imperial College London
- Keith Hannabuss University of Oxford
- Leonard Hardiman University of Bath
- Yang-Hui He City University, London; University of Oxford
- Pedram Hekmati IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro; University of Auckland
- Robin Hillier
- Yusuke Isono Kyoto University
- Masaki Izumi Kyoto University
- Arthur Jaffe Harvard University
- Vaughan Jones Vanderbilt University; University of California, Berkeley
- Corey Jones Australian National University
- Evgenios Kakariadis University of Newcastle upon Tyne
- Yasu Kawahigashi University of Tokyo
- Alastair King University of Bath
- David Kyed University of Southern Denmark
- Gandalf Lechner Cardiff University
- Gus Isaac Lehrer University of Sydney
- Xin Li
- Ying-Fen Lin Queen's University Belfast
- Zhengwei Liu
- Roberto Longo Università degli Studi di Roma Tor Vergata
- Lilit Martirosyan Max-Planck-Institut für Mathematik, Bonn
- Andrew McKee Queen's University Belfast
- Anna Mkrtchyan University of Edinburgh
- Andrew Monk University of Glasgow
- Stephen Moore Cardiff University
- Vincenzo Morinelli Università degli Studi di Roma Tor Vergata
- Scott Morrison Australian National University
- Ryo Nojima University of Tokyo
- Denjoe O'Connor Dublin Institute for Advanced Studies
- Yoshiko Ogata University of Tokyo
- Sebastien Palcoux Institute of Mathematical Sciences, Chennai
- David Penneys University of California, Los Angeles
- Ulrich Pennig Cardiff University
- N. Christopher Phillips University of Oregon
- Mathew Pugh Cardiff University
- Sven Raum EPFL - Ecole Polytechnique Fédérale de Lausanne
- Jonathan Rosenberg University of Maryland, College Park
- Stefano Rossi Università degli Studi di Roma Tor Vergata
- Ingo Runkel King's College London
- Hubert Saleur University of Southern California
- Koichi Shimada Kyoto University
- Paul Smith University of Washington
- Noah Snyder Indiana University
- Yoh Tanimoto Università degli Studi di Roma Tor Vergata
- Constantin Teleman University of Oxford
- James Tener University of California, Santa Barbara
- Aaron Tikuisis University of Aberdeen
- Ivan Todorov Queen's University Belfast
- Henry Tucker University of California, San Diego
- Stefaan Vaes KU Leuven
- Leonid Vainerman Université de Caen Basse-Normandie
- Alina Vdovina Newcastle University
- Roland Vergnioux Université de Caen Basse-Normandie
- Christian Voigt University of Glasgow
- Katrin Wendland Albert-Ludwigs-Universität Freiburg
- Hans Wenzl University of California, San Diego
- Stuart White University of Glasgow
- Feng Xu
- Shigeru Yamagami Nagoya University
- Mayuko Yamashita University of Tokyo
- Makoto Yamashita Ochanomizu University
- Joachim Zacharias University of Glasgow
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