Details of Grant 

EPSRC Reference:	GR/S80592/01
Title:	Modular invariants and subfactors
Principal Investigator:	Evans, Professor DE
Other Investigators:
Researcher Co-Investigators:
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Department:	Sch of Mathematics
Organisation:	Cardiff University
Scheme:	Standard Research (Pre-FEC)
Starts:	16 January 2004	Ends:	15 July 2006	Value (£):	10,009
EPSRC Research Topic Classifications:	Algebra & Geometry Mathematical Analysis Mathematical Physics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
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Panel History:
Summary on Grant Application Form
The classification of braided subfactors in the theory of von Neumann algebras and the classification of modular invariants in rational conformal field theoryare richly interwined yet mysterious. Here we bring togther two workers with complementary backgrounds to obtain a deeper understanding of these relationships. In its simplest form, this relates the ADE classification of subfactors with Jones index less than four with the ADE classification of Capelli, Itzykson and Zuber of SU(2) modular invariants.However, modular data and corresponding subfactors and modular invariants arise also naturally in other contexts - not only affine algebras and the quantum doubles of finite groups but quantum doubles of exotic subfactors of finite depth, quasi rational theories and vertex operator algebras.The classification of braided subfactors in the theory of von Neumann algebras and the classification of modular invariants in rational conformal field theoryare richly interwined yet mysterious. Here we bring togther two workers with complementary backgrounds to obtain a deeper understanding of these relationships. In its simplest form, this relates the ADE classification of subfactors with Jones index less than four with the ADE classification of Capelli, Itzykson and Zuber of SU(2) modular invariants.However, modular data and corresponding subfactors and modular invariants arise also naturally in other contexts - not only affine algebras and the quantum doubles of finite groups but quantum doubles of exotic subfactors of finite depth, quasi rational theories and vertex operator algebras.
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