EPSRC Reference: 
EP/V013203/1 
Title: 
Workshop on Operator Algebras: Subfactors, KTheory and Conformal Field Theory 
Principal Investigator: 
Lechner, Dr G 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Sch of Mathematics 
Organisation: 
Cardiff University 
Scheme: 
Standard Research 
Starts: 
01 August 2021 
Ends: 
31 October 2022 
Value (£): 
18,585

EPSRC Research Topic Classifications: 
Mathematical Analysis 
Mathematical Physics 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Research in von Neumann algebras, originally studied by Murray and von Neumann in order to set up a mathematically rigorous formulation of quantum mechanics, received a major boost with the study of subfactors initiated by Vaughan Jones in the early 1980's. Subfactor theory rapidly led to connections with link and 3manifold 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 (CFT), with impressive 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.
The focus of this workshop is on shaping the future research directions in operator algebras, bringing together experts from such diverse disciplines as subfactor theory, Ktheory and CFT, who will consider solutions to identified problems through a combination of lectures and participative sessions of breakout groups. The topics of the workshop include:
 The connections between the different formulations of chiral CFTS (local conformal nets, vertex operator algebras, Segal framework).
 The reconstruction programme  realisation of a chiral CFT which reproduces a given modular tensor category.
 Quantum symmetries on C*algebras.
 Higher equivariant twists as equivariant Fell bundles.
 Connections between von Neumann relative entropy in CFT, subfactors, and mathematical physics.
The workshop will bring together researchers at the beginning of their careers with experts who were instrumental in finding applications of von Neumann algebras, including Jones and Voiculescu who have already agreed to speak. Von Neumann algebras, subfactors, Ktheory and CFT have had a huge influence on the study of group representations, algebraic topology and across theoretical physics in the past. In a future in which quantum theory is rapidly becoming a fundamental part of everyday technology, the applications of operator algebras is expanding and can be expected to develop new applications for a new generation.

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Further Information: 

Organisation Website: 
http://www.cf.ac.uk 