Details of Grant 

EPSRC Reference:	GR/M87986/01
Title:	FREE PROBABILITY AND SUBFACTORS
Principal Investigator:	Evans, Professor DE
Other Investigators:	Bockenhauer, Dr J
Researcher Co-Investigators:
Project Partners:
Department:	Sch of Mathematics
Organisation:	Cardiff University
Scheme:	Standard Research (Pre-FEC)
Starts:	01 October 2000	Ends:	30 September 2003	Value (£):	5,500
EPSRC Research Topic Classifications:	Mathematical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
Connections between analytical aspects of number theory andvon Neumann algebras of discrete groups-realized by using a new representation for the algebra of PSL(2,Z) and its subgrou s obtained by the identification of Toeplitz operators whoses symbols are (arithmatic) automorphic forms with interwining operators between different representations of the modular groups, or more general Fuchsian groups. The classical Toeplitz operators; symbols are invarient under a Fuchsian group have continuous, (Breuer)indices,and.it is interesting to have an unifying approach containing both the finite and infinit covolume case.. Dykema and'' Radulescu have independently discovered how to define the algebra of a free group with. fractional number of generators -. Radulescu, this number is a bijective function on the Planck deformation constant in the Berezin quantization of the upper halfplane. Consequently one may differentiate with respect to'the number of generators (using the cyclic cohomology of Connes). Radulescuintends to develop the relation between this aspect and the Von Neumann question on the isomorphism class of a free group factor. To develop a theory of nets of reee subfactors and apply the theory of alpha induction developed by Bockenhauer and Evans to such nets and understand the role of modular invariant partition functions. To understand the role of discrete Hecke subgroups of PSL (2R)in the discrete values of the Jones index and the role of finite subgroups of SL(2C) in the theory of subfactors.
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