D. Sean Fitzpatrick Department of Mathematics and Computer Science Mount Allison University Email:  sfitzpatrick at mta dot ca

Update: My contract at Mount Allison ends on the 30^th of June. In August I will begin an NSERC postdoctoral fellowship, which I will be taking to the University of California, Berkeley. Between Mount Allison and Berkeley will be a trip down the Cabot Trail, the Poisson 2010 conference in Rio de Janeiro, and about 6,500 kilometres worth of driving in a more or less westerly direction.

I am currently an assistant professor in the Department of Mathematics and Computer Science at Mount Allison University, which is located in Sackville, New Brunswick.

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.
Details of this work can be found in the two preprints listed below. For a summary, see my research statement.

To my CV .

Information about my more famous namesake on Wikipedia.
(By coincidence I play the same sport, in the same position, but not at anything near the same skill level!)

Education

PhD: University of Toronto, 2009.
Advisor: Eckhard Meinrenken.
Thesis: Almost CR Quantization via the Index of Transversally Elliptic Dirac Operators.

MSc: University of Toronto, 2004.
Department: Mathematics.
Area: Symplectic geometry.
Master's advisor: Lisa Jeffrey.

BSc: University of Winnipeg, 2003.
Majors: Mathematics and Physics.

Teaching

Fall 2009:
MATH1111 - Calculus I
MATH2111 - Multivariable Calculus

Winter 2010:
MATH1111 - Calculus I
MATH2121 - Elementary Differential Equations
MATH4131 - Complex Variables with Applications

Past courses

For links to courses I taught at the University of Toronto, see the U of T version of this webpage.

Publications and preprints

S. Fitzpatrick, Some remarks on the geometric quantization of contact manifolds, preprint.

S. Fitzpatrick, An equivariant index formula for almost-CR manifolds, preprint. Now published online in Int. Math. Res. Not.

S. Fitzpatrick, An equivariant index formula for elliptic actions on contact manifolds, preprint. Published in Math. Res. Let.

Links

MathSciNet
The arXiv
Mount Allison University
Department of Mathematics, U of T
The University of Winnnipeg
Google (Scholar)
Ubuntu