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: PDF format
Research: Below are preprints of my research papers:
  1. The Spectra of Certain Classes of Room Frames: The Last Cases
    Joint with J. Dinitz
    Submitted.
  2. ...a modified inverse Kostka matrix
    Joint with E. Egge and N. Loehr
    Submitted.
  3. A combinatorial version of Sylvester's four-point problem
    To appear in Adv. in App. Math.
  4. A continuous family of partition statistics equidistributed with length
    Joint with N. Loehr
    J. Combin. Theory Ser. A 116 (2009), no. 2, 379--403. (final version)
  5. Nested quantum Dyck paths and nabla(s_lambda)
    Joint with N. Loehr
    International Mathematics Research Notices 2008; Vol 2008: article ID rnm157 (final version)
  6. Bitableaux bases for Garsia-Haiman modules of hollow type
    Joint with E. Allen and M. Cox
    J. Combin. Theory Ser. A 115 (2008), no. 7, 1127--1155.
  7. A human proof for a generalization of Shalosh B. Ekhad's 10^n Lattice Paths Theorem
    Joint with N. Loehr and B. Sagan
    Ars Combin. 89 (2008), 421--429.
  8. Square q,t-lattice paths and nabla(p_n)
    Joint with N. Loehr
    Transactions of the AMS, 359 (2007) no. 2, 649-669.
  9. The combinatorics of a three-line circulant determinant
    Joint with N. Loehr and H. Wilf
    Israel Journal of Mathematics 143 (2004), 141-156
  10. Juggling probabilities
    American Mathematical Monthly 112, no. 2 (2005), 105-118
  11. Counterexamples to the 0,1-Conjecture
    Joint with T. McLarnan
    Represent. Theory 7 (2003), 181-195 (final version)
  12. A formula for inverse Kazhdan-Lusztig polynomials in S_n.
    J. Comb. Theory A, Vol. 104, Iss. 2 , November (2003), 301-316 (final version)
  13. 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)
  14. Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permuations.
    Joint with S. Billey
    J. of Alg. Comb., 13 (2): 111-136, March 2001 (final version)
Misc: Below are some other writings:
  1. The shape of a pool.
    Eternally in preparation.
  2. A Photographic Assignment for Abstract Algebra
    To appear in PRIMUS.
  3. Juggling Performers + Math = ?
    Math Horizons, Feb. 2008.
  4. Randomized voting and A sketch of randomized voting.
    In limbo.
Talks: Here are the overheads for some of the talks I have given:
  1. An infinite family of partition statistics
    Penn State AMS Sectional Meeting; Oct. 2009
  2. "Statistics" in Combinatorics
    Invited talk, MathFest Aug. 2009 in Portland, OR
  3. A variation on Sylvester's four-point problem
    Gems of Combinatorics Session, MathFest Aug. 2009 in Portland, OR
  4. Combinatorial structures associated to the nabla operator
    Banff, Sep. 2007 (Jim Haglund, proxy speaker; thanks Jim!)
  5. Combinatorial aspects of nabla(s_lambda)
    given at CRM, Montreal in May 2007.
  6. Square q,t-lattice paths and nabla(p_n)
    given at FPSAC '05 in Taormina, Sicily in June 2005.
  7. Overview of Kazhdan-Lusztig Polynomials
    given at UPenn combinatorics seminar in October 2003.
  8. Counterexamples to the 0,1-Conjecture
    given at the Computational Lie Theory conference at CRM in June 2002.
  9. Maximal Singular Loci for Schubert Varieties in SL(n)/B
    given at FPSAC '01 meeting in Scottsdale, AZ in May 2001.
  10. Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations
    given at the Joint Meeting in Washington, DC in January 2000.
Thesis: Here is my doctoral thesis.
My thesis advisor was Sara Billey at MIT (now at Univ. Washington). 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: From F01 to S03 I was a postdoc at the University of Massachusetts at Amherst. From F03 to S04 I was an NSF postdoctoral fellow at the University of Pennsylvania. From F04 to F08 I was an Assistant Professor at Wake Forest University in Winston-Salem, NC. In S09 I started my current position of Assistant Professor at the University of Vermont in Burlington, Vermont.