Area of research
My research is in the area of the representation theory of groups, more specifically in the modular representation theory of algebraic and finite symmetric groups. As of this writing (1 September 2010), the Wikipedia article on modular representation theory is a reasonable guide to understanding what the words mean, though the writing needs a little work.
For the last several years, I have been mostly working on combinatorial questions that arise in the representation theory work. This involved counting various combinatorial objects like partitions that satisfy certain conditions.
PublicationsNote: The papers that are available here are in pdf format. You'll need Adobe Acrobat or a newer version of ghostscript.
- Disconnected linear groups and restrictions of representations, Groups of Lie Type and Their Geometries (William Kantor, ed.), Cambridge University Press, 1995, pp. 111-116.
- Irreducible restrictions of representations of the symmetric groups, Bull. London Math. Soc. 27 (1995), 453-459.
- Overgroups of irreducible linear groups, I, J. Algebra 181 (1996), 26-69.
- A proof of the Mullineux conjecture (with Alexander Kleshchev), Math. Z. 226 (1997), 267-308.
- Overgroups of irreducible linear groups, II, Trans. Amer. Math. Soc. 351 (1999), 3869-3914.
- Irreducible representations of the alternating group in odd characteristic, Proc. Amer. Math. Soc. 125 (1997), 375-380.
- Practice Makes Proficient: Ohio Fourth Grade Mathematics Proficiency Study Guide, Cleveland Education Fund, 1997.
- Confusing clocks (with Cory Franzmeier and Richard Gayle), Math. Mag. 71 (1998), 190-195.
- Logarithmic differentiation: two wrongs make a right (with N. Sam Brannen), College Math. Journal 35 (2004), 388-390.
- Self-conjugate t-core partitions, sums of squares, and p-blocks of An (with John Baldwin, Melissa Depweg, Abraham Kunin, Lawrence Sze), J. Algebra 297 (2006), 438-452.
- Self-conjugate simultaneous p- and q-core partitions and blocks of An (with Hoàng Mai and Lawrence Sze), J. Number Theory 129 (2009), 858-865.