Grant: Discovery Grants Program - Individual

This is a proposal for research that concerns the study of certain objects called von Neumann algebras. These were first studied in the 1930's by John von Neumann in connection with quantum physics, and they are distinguished by the idea of continuous dimensionality.In the 1980's, using von Neumann's theory ---and in the course of a striking discovery linking the field of knot theory and statistical mechanics--- Vaughan Jones studied inclusions N in M of special von Neumann algebras called II_1 factors. He introduced an invariant for the inclusion N in M up to conjugacy by automorphisms: This is a real number, called the index for N in M, which enable us to distinguish pairs N in M that are not conjugate. Since then, more invariants were defined in order to attempt to characterise these inclusions.The general objectives of this proposal are related to contructing and studying certain inclusions of hyperfinite II_1 factors by computing finite invariants.