Professor, appointed 2002 (Ph.D. UC San Diego 1994)
On leave: Spring '13
Research area: Algebraic combinatorics, Lie theory and computational geometry
Personal Web page: http://www.math.washington.edu/~billey/
Office: PDL C-445
Hobbies: Volleyball, unicycling, puzzles, hiking, bicycling, and generally exploring Washington State parks
My research is in algebraic combinatorics. Combinatorics is the study of counting and bijective proofs, so an algebraic combinatorialist counts algebraic objects. In particular, I am interested in Schubert polynomials, Schubert varieties, flag manifolds, Kazhdan-Lusztig polynomials, Stanley symmetric functions, Bruhat order, Weyl group and root systems of all types etc. I am a strong advocate of using computers to do math research, in particular for obtaining data for conjectures and computer verified proofs.
Smoothness of Schubert Varieties via Patterns in Root Systems . Joint with Alex Postnikov. To appear in Advances in Applied Math.
A vector partition function for the multiplicities of sl_k(C). Joint with Etienne Rassart and Victor Guillemin. Journal of Algebra, 278 (2004) no. 1, 251-293.
Lower bounds for Kazhdan-Lusztig polynomials from patterns . Joint with Tom Braden. Transform. Groups 8 (2003) no. 4, 321-332.
Maximal Singular Loci of Schubert Varieties in SLn/B (with Gregory Warrington) in Trans. AMS. 355 (2003), no. 10, 3915-3945.
Kostant Polynomials and the Cohomology Ring for G/B. Duke Journal of Math, 96, No. 1, pp. 205-224, 1998. This is the extended version of the announcement that appeared in the Proceedings of the National Academy of Science.
Schubert Polynomials for the classical groups , Sara Billey and Mark Haiman. Journal of AMS, 8, Number 2, April 1995
Some Combinatorial Properties of Schubert Polynomials , Sara Billey, Richard Stanley, and William Jockusch. J. of Algebraic Comb. 2 Num. 4, 1993.
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