Operator algebras: subfactors and their applications

Operator algebras: subfactors and their applications's image
Created: 2017-02-01 15:11
Institution: Isaac Newton Institute for Mathematical Sciences
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.
 

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A classification of some 3-Calabi-Yau algebras

   14 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

   20 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

   23 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

   46 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


An application of T-duality to K-theory

   9 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

   36 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

   359 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

   9 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

   11 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

   37 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

   14 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

   18 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

   22 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

   17 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

   20 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

   12 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

   32 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

   12 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


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