Workshop on Operator Algebras: Subfactors, K-Theory and Conformal Field Theory

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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 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 (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, K-theory 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, K-theory 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.