Sara Billey's homepage
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Prof. SARA BILLEY
Department of Mathematics
Padelford C-445
University of Washington
Box 354350
Seattle, WA 98195-4350
Phone: 206-616-3107
Fax: 206-543-0397
email: billey at-sign math.washington.edu
Current Projects
I am an Associate Professor of Mathematics at the University of Washington in the
sometimes sunny
city of
Seattle. Here are some of my current projects
- Teaching: This fall and winter I will be teaching a course for
graduate students called
Math 582:
Foundations of Combinatorics.
Chris Hoffman will teach the third
quarter of this course on Probabalistic Combinatorics.
- Seminar: I organize the Combinatorics Seminar at
UW with Isabella Novik and
Michael Goff.
- Editing: I am an editor for Advances in Math. If you would
like to submit something to the journal, please use the web
site. We are looking for high quality papers with wide
appeal.
-
Zometool Competition: I host the annual Zometool Competition for
SIMUW;
our high school math camp.
-
Mathday: I speak (almost) every year at Mathday; one of the biggest
mathematical events for high school students in the country
where 1200 students come to campus for a smogsbord of
mathematical experiences. This year my topic will be "Sudoku"
which has a lot to do with math despite what some publishers claim.
-
AMS Special Session:
Alexander Kleshchev, Stephanie van Willigenburg and I are
organizing a special session on Combinatorial
Representation Theory as part of the AMS 2008 Fall Western
Section Meeting, to be held at the University of British Columbia,
Vancouver, on October 4-5, 2008.
Research Overview
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.
Books
- Singular Loci of Schubert Varieties (joint with Lakshmibai)
in series Progress in Mathematics, Birkhauser Boston, v. 182,
2000. NOW AVAILABLE from Amazon and a book store near you!! (No, I
did not pay those people for their reviews.)
Upcoming/Recent Talks
Recent Publications, Preprints
Also, check the
Mathematics ArXiv
- Affine partitions and affine Grassmannians with
Steve Mitchell. Preprint. Computer code in lisp and Maple
- Smooth
and palindromic Schubert varieties in affine Grassmannians. with
Steve Mitchell. Preprint.
-
Embedded factor patterns for Deodhar elements in Kazhdan-Lusztig theory
with Brant Jones to appear in the Special Issue of Annals of Combinatorics dedicated to
Permutation Patterns, 2008.
-
Flag arrangements and triangulations of products of
simplicies
with Federico Ardila. Advances in Math. 214 (2007), no. 2, 495--524. 32S22 (14M15).
-
Intersections of Schubert varieties and other permutation
array schemes with Ravi Vakil. IMA Volumes in Mathematics and its Applications
Volume 146: Algorithms in Algebraic Geometry, 2007, pages 21--54. Code for
experimentation is available here.
- Smoothness of Schubert
Varieties via Patterns in Root Systems
. Joint with Alex Postnikov. Advances in Applied Math v. 34
(2005) p. 447-466.
- A
vector partition function for the multiplicities of
sl_k(C). Joint with Etienne Rassart and Victor
Guillemin. Journal of Algebra, vol. 278 (2004) no. 1, 251-293.
- Lower bounds for
Kazhdan-Lusztig polynomials from patterns
. Joint with Tom Braden. Transform. Groups vol. 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.
- Kazhdan-Lusztig Polynomials for
321-hexagon-avoiding permutations, (with Gregory Warrington) in J. of Algebraic Combinatorics, v. 13 (2001), no. 2, 111--136.
- The Parabolic map. (joint
with Ken Fan and Jozsef Losonczy) J. of Alebra, vol. 214 (1999).
- Kostant Polynomials and the
Cohomology Ring for G/B. Duke Journal of Math, Volume
96, No. 1, pp. 205-224, 1999. This is the extended version of the
announcement that appeared in the Proceedings of the National Academy
of Science.
- Kostant Polynomials and the
Cohomology Ring for G/B Proceedings of the
National Academy of Science, Jan.1997.
- Pattern Avoidance and Rational
Smoothness of Schubert varieties. Advances
in Math, vol. 139 (1998) pp. 141--156.
-
Vexillary elements of the hyperoctahedral group
Sara Billey and Tao Kai Lam. J. of Algebraic Combinatorics, v.8
(1998) pp. 139-152.
Lisp code is available upon request for verifying
the computer aided proof in this paper.
-
Transition Equations for Isotropic Flag Manifolds.
Discrete Math., Special Issue devoted
to the Conference in Taormina, Sicilly, in honor of Adriano
Garsia, vol. 193 (1998) pp. 69--84.
-
Schubert Polynomials for the classical groups ,
Sara Billey and Mark Haiman
Journal of AMS Volume 8, Number 2, April 1995
- RC-Graphs and Schubert polynomials
Nantel Bergeron and Sara Billey
Experimental Mathematics, Vol.2 (1993), No. 4. Available
upon request.
-
Some Combinatorial Properties of Schubert Polynomials ,
Sara Billey, Richard Stanley, and William Jockusch
J. of Algebraic Comb.
Vol. 2 Num. 4, 1993.
- An Abstract Definition of Schubert Polynomials.
University of California, San Diego, Ph.D. thesis 1994.
Available upon request.
Consulting Policy
I am available as a mathematical
consultant for a couple weeks per year. I analyze combinatorial
problems, lecture on special topics, answer standard math questions,
do literature reviews etc. The fee will be $1500 for the first day,
paid up front. While I understand that this fee is high, I feel it is
justified since I will have to take time away from my research and my
students (who pay about $100/hour each).
Current and Former Ph.D Students
Other Fun Stuff
- Women
in Mathematics: This is a history of women in mathematics going
back to the fifth century B.C.
- Grandma
My grandma is on display at the Smith-Zimmermann Museam Homepage.
She is the one in the carriage.
- Check out Jack Lee's web page on cool things to do in Seattle. I
have visited almost every place on this list and recommend them all.