department of mathematics
Ph.D. Ohio State University 1988
Lie groups are groups of continuous symmetries; they are classified similiarly to the
Platonic solids. Galois groups are the symmetries of the roots of polynomials. Representation
Theory is the study of the different ways particular symmetries manifest.
The Langlands Program investigates conjectural correspondences between infinite
dimensional representations of Lie groups and finite dimensional representations of
Galois groups. We seek new and explicit examples of this correspondence.
- Formal degrees and L-packets of unipotent discrete series representations of
exceptional p-adic groups, Crelle’s Journal 520, (2000), pp. 37-93.
- From Laplace to Langlands via representations of orthogonal groups,
with B. Gross, Bull. Amer. Math Soc., 43 (2006), pp.163-205.
- On the restriction of Deligne-Lusztig characters, Jour. Amer. Math. Soc., 20, (2007), pp.573-602
- Supercuspidal L-packets of positive depth and twisted Coxeter elements,
Crelle’s Journal 620, (2008), pp. 1-33.
- Depth-zero supercuspidal L-packets and their stability,
with S. DeBacker, Annals of Math., 169, No. 3, (2009), pp. 795–901.