Sara Billey

Professor, appointed 2002 (Ph.D. UC San Diego 1994)

Research area: Algebraic combinatorics, Lie theory and computational geometry

Personal Web page: http://www.math.washington.edu/~billey/
E-mail: billey[_a_t_]math.washington.edu
Phone: 616-3107
Office: PDL C-445
Courses taught this quarter: MATH 581 B

Hobbies: Volleyball, unicycling, puzzles, hiking, bicycling, and generally exploring Washington State parks

Professional interests

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.

Selected bibliography

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.