My current position is a full-time teaching position, and I am no longer active in research. My area of reseach during my PhD and postdoctoral studies was differential geometry; in particular, I studied symplectic, Poisson, contact and CR geometry, and analogues of these, especially in the context of quantization, index theory and "Dirac-like" operators. While I was at Western I ran a year-long learning seminar on the Atiyah-Singer index theorem, with the goal of understanding the index of transversally elliptic operators and the infinitesimal index of de Concini, Procesi, and Vergne.
(First links are to preprint versions on arxiv.org, with link to the published version beneath.)
S. Fitzpatrick, On the geometry of almost S-manifolds.
ISRN Geometry, vol. 2011, Article ID 879042, 12 pages, 2011, DOI:10.5402/2011/879042. http://www.isrn.com/journals/geometry/2011/879042/.
S. Fitzpatrick, On transversally elliptic operators and the quantization of manifolds with f-structure.
Mediterranean Journal of Mathematics 10, Issue 1, pp. 449-473 (2013). http://link.springer.com/article/10.1007/s00009-011-0168-y, DOI:10.1007/s00009-011-0168-y.
S. Fitzpatrick, On the geometric quantization of contact manifolds.
Journal of Geometry and Physics 61 (2011), pp. 2384-2399. http://dx.doi.org/10.1016/j.geomphys.2011.07.011.
S. Fitzpatrick, An equivariant index formula for almost CR manifolds.
International Math. Research Notices 2009 no. 18 (2009), pp. 3366-3390. http://imrn.oxfordjournals.org/cgi/content/abstract/rnp057?ijkey=RzzB46XRfSIpNiI&keytype=ref
S. Fitzpatrick, An equivariant index formula in contact geometry.
Math. Research Letters 16 no. 3 (2009), pp. 375-394. http://www.mrlonline.org/mrl/2009-016-003/