# Operator algebras: subfactors and their applications

Created: | 2017-02-01 15:11 |
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Institution: | Isaac Newton Institute for Mathematical Sciences |

Editors' group: | SMS Editors group for the Newton Institute |

Description: | 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. |

# Media items

This collection contains 112 media items.

### Media items

#### A classification of real-line group actions with faithful Connes--Takesaki modules on hyperfinite factors

14 views

Shimada, K (Kyoto University)

Tuesday 24th January 2017 - 16:00 to 17:00

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 8 Feb 2017

#### A classification of some 3-Calabi-Yau algebras

16 views

Smith, P (University of Washington)

Wednesday 29th March 2017 - 10:00 to 11:00

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 4 Apr 2017

#### A diagrammatic approach to Ocneanu cells

21 views

Bigelow, S (University of California, Santa Barbara)

Monday 23rd January 2017 - 11:30 to 12:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 8 Feb 2017

#### A geometric approach to constructing conformal nets

36 views

Tener, J (University of California, Santa Barbara)

Monday 27th March 2017 - 14:30 to 15:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 28 Mar 2017

#### A relative tensor product of rational full conformal field theories

47 views

Kawahigashi, Y (University of Tokyo)

Tuesday 21st March 2017 - 14:00 to 15:00

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 13 Apr 2017

#### Algebras, automorphisms, and extensions of quadratic fusion categories

18 views

Pinhas Grossman

Friday 27th January 2017 - 11:30 to 12:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 9 Feb 2017

#### An application of T-duality to K-theory

11 views

Hekmati, P (IMPA - Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, University of Auckland)

Wednesday 14th June 2017 - 10:00 to 11:00

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 30 Jun 2017

#### An elementary approach to unitary representations of the Thompson group F

40 views

Kostler, C (University College Cork)

Thursday 26th January 2017 - 13:30 to 14:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 9 Feb 2017

#### Approximate equivalence of measure-preserving actions

360 views

Aaserud, A (Cardiff University)

Thursday 9th March 2017 - 14:00 to 15:00

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 20 Mar 2017

#### Associative algebras and conformal field theories

13 views

Saleur, H (University of Southern California)

Tuesday 13th June 2017 - 11:30 to 12:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 30 Jun 2017

#### Baxterising using conserved currents

26 views

Fendley, P (University of Oxford)

Tuesday 13th June 2017 - 13:30 to 14:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 30 Jun 2017

#### Bicommutant categories

49 views

Henriques, A (University of Oxford, Universiteit Utrecht)

Thursday 15th June 2017 - 14:30 to 15:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Mon 3 Jul 2017

#### Bivariant and Dynamical Versions of the Cuntz Semigroup

16 views

Zacharias, J (University of Glasgow)

Tuesday 6th June 2017 - 12:45 to 13:45

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 28 Jun 2017

#### Braids, Cosimplicial Identities, Spreadability, Subfactors

24 views

Gohm, R (Aberystwyth University)

Thursday 26th January 2017 - 14:30 to 15:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 9 Feb 2017

#### Buildings and C*-algebras

23 views

Vdovina, A (Newcastle University)

Thursday 26th January 2017 - 11:30 to 12:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 9 Feb 2017

#### Calabi-Yau volumes and Reflexive Polytopes

18 views

He, Y-H (City University, London, University of Oxford)

Friday 31st March 2017 - 14:30 to 15:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 4 Apr 2017

#### Classification of free Araki-Woods factors

22 views

Vaes, S (KU Leuven)

Wednesday 25th January 2017 - 10:00 to 11:00

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 8 Feb 2017

#### Coefficients for commutative K-theory

13 views

Gritschacher, S (University of Oxford)

Friday 31st March 2017 - 11:30 to 12:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 4 Apr 2017

#### Cohomology and L2L2-Betti numbers for subfactors and quasi-regular inclusions

33 views

Shlyakhtenko, D (University of California, Los Angeles)

Wednesday 25th January 2017 - 11:30 to 12:30

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 8 Feb 2017

#### Conformal covariance and the split property

13 views

Morinelli, V (Università degli Studi di Roma Tor Vergata)

Thursday 9th February 2017 - 14:00 to 15:00

**Collection**:
Operator algebras: subfactors and their applications

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 15 Feb 2017