B.Sc. (Dalhousie University)
M.Phil. (University of Edinburgh)
Ph.D. (Dalhousie University)
Werner Heisenberg asserted that physical quantities are governed by non-commutative algebra. Operator algebras are non-commutative algebras of operators on a Hilbert space. These algebras arise in the study of group representations, dynamical systems, statistical and quantum mechanics.
The study of operator algebras is an interesting blend of ideas from operator theory, measure theory, dynamical systems, algebraic topology, probability theory, and differential geometry.
In recent years I have been working on non-commutative probability. Non-commutative probability is a new branch of the operator algebra family in which ideas from random matrices and probability theory are applied to operator algebras.