Home Up Greg Warrington: Research

Research


Interests: My interests are algebraic combinatorics, Kazhdan-Lusztig polynomials, Schubert varieties, combinatorics of Weyl groups, and diagonal harmonics.
CV: Postscript and PDF
Writings: Below are preprints of my papers:
  1. The coefficient of the linear term of Kazhdan-Lusztig polynomials in S_n
    In preparation.
  2. (2004) The combinatorics of a three-line circulant determinant and a pdf version (pdf)
    Joint with N. Loehr and H. Wilf
    Israel Journal of Mathematics (to appear)
  3. (2004) Juggling probabilities and a pdf version (pdf)
    American Mathematical Monthly (to appear)
  4. (2003) Counterexamples to the 0,1-Conjecture
    Joint with T. McLarnan
    Represent. Theory 7 (2003), 181-195 (final version)
  5. (2003) A formula for inverse Kazhdan-Lusztig polynomials in S_n.
    J. Comb. Theory A, Vol. 104, Iss. 2 , November (2003), 301-316 (final version)
  6. (2001) Maximal singular loci for Schubert varieties in SL(n)/B.
    Joint with S. Billey
    Trans. AMS 355 (2003), no. 10, 3915--3945 (electronic) (final version)
  7. (2000) Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permuations.
    Joint with S. Billey
    J. of Alg. Comb., 13 (2): 111-136, March 2001 (final version)
Talks: Here are the overheads for some of the talks I have given:
  1. Overview of Kazhdan-Lusztig Polynomials
    given at UPenn combinatorics seminar in October 2003. Here is a pdf version
  2. Counterexamples to the 0,1-Conjecture
    given at the Computational Lie Theory conference at CRM in June 2002.
  3. Maximal Singular Loci for Schubert Varieties in SL(n)/B
    given at the FPSAC '01 meeting in Scottsdale, AZ in May 2001.
  4. Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations
    given at the Joint Meeting in Washington, DC in January 2000.
Thesis: Here is my thesis.
My thesis advisor was Sara Billey at MIT. You can check out my mathematical genealogy at The Mathematics Genealogy Project.
Code: If you want to compute type A Kazhdan-Lusztig polynomials,
then do I have the program for you
Trajectory: This year I am an NSF postdoctoral fellow at the University of Pennsylvania. I have accepted a tenure-track position at Wake Forest University in Winston-Salem, NC commencing in the fall of 2004.