I did my PhD studies in mathematics at the University of Toronto, under the advising of Eckhard Meinrenken.
My thesis work involves the application of the equivariant index theorem for transversally elliptic operators to a class of differential operators that can be constructed on any manifold equipped with an almost CR (Cauchy-Riemann) structure. A copy of my thesis is available here.
In the particular case of a contact manifold, this can be interpreted as a "quantization" procedure analogous to geometric quantization in symplectic geometry. When applied to complex homogeneous spaces, the resulting index formula includes character formulas for both the L2 and holomorphic induced representations as special cases.
Advisor: Eckhard Meinrenken.
Thesis: Almost CR Quantization via the Index of Transversally Elliptic Dirac Operators.
Department: Mathematics.
Area: Symplectic geometry.
Master's advisor: Lisa Jeffrey.
Majors: Mathematics and Physics.