Research interests: My research is in algebraic combinatorics. The core principle of algebraic combinatorics is that enumerative results are often shadows of rich algebraic and geometric structures. Therefore enumerative results can be derived from these structures, but they can also be used to identify them. Both of these currents underly my work, which mostly focuses on symmetric functions and the combinatorics of Coxeter groups. I am especially interested in applications to Schubert calculus. I've always had a soft spot for discrete probability and am also currently working on a project on orthogonal polynomials.

Collaborators: I have had the privilege of working with many outstanding mathematicians, including: Sara Billey (Scholar profile), Eric Marberg (Scholar profile), Rebecca Patrias, Brendan Pawlowski (Scholar profile), Oliver Pechenik (Scholar profile), Victor Reiner, Austin Roberts, Nathan Williams (Scholar profile), Benjamin Young


Publications:

You can find up-to-date versions of my papers and preprints at the arXiv and Google Scholar.

  1. Weak order and descents for monotone triangles (with V. Reiner) submitted.
  2. Atoms for signed permutations (with E. Marberg) submitted.
  3. Fixed-point-free involutions and Schur P-positivity (with E. Marberg and B. Pawlowski) to appear, Journal of Combinatorics.
  4. Transition formulas for involution Schubert polynomials. (with E. Marberg and B. Pawlowski) Selecta Mathematica, Volume 24, Issue 4, pp 2991--3025.
  5. Involution words: counting problems and connections to Schubert calculus symmetric orbit closures (with E. Marberg and B. Pawlowski) Journal of Combinatorial Theory Series A, Volume 160, pp 217--260.
  6. Doppelgangers: Bijections of Plane Partitions (with B. Patrias, O. Pechenik and N. Williams) International Mathematics Research Notices (rny018) pp. 1--54.
  7. Schur P-positivity and involution Stanley symmetric functions (with E. Marberg and B. Pawlowski) International Mathematics Research Notices (rnx274) pp. 1–-52.
  8. Involution Schubert-Coxeter combinatorics (with E. Marberg and B. Pawlowski) Séminaire Lotharingien de Combinatoire, 78B.51 (2017), 12 pp (extended abstract, FPSAC 2017).
  9. Shifted Hecke insertion and the K-theory of OG(2n+1) (with A. Keilthy*, R. Patrias, L. Webster*, Y. Zhang* and S. Zhou*) Journal of Combinatorial Theory, Series A Volume 151, October (2017) 207--240 (extended abstract in FPSAC 2017)
  10. Involution words II: braid relations and atomic structures (with E. Marberg and B. Pawlowski) Journal of Algebraic Combinatorics Volume 45, Issue 3 (2014) 701--743
  11. Subwords and plane partitions (extended abstract), DMTCS proc. FPSAC’15 (2015) 241–252.
  12. Coxeter-Knuth graphs and a signed Little map for type B reduced words (with S. Billey, A. Roberts and B. Young), Electronic Journal of Combinatorics 21 (2014) Issue 4.
  13. Relating Edelman-Greene insertion to the Little map (with B. Young), Journal of Algebraic Combinatorics Volume 40, Issue 3 (2014) 693-710 (extended abstract appeared in FPSAC '13)
    * indidcates undergraudate coauthor

    Thesis:

    • Bijective combinatorics of reduced decompositions, Ph.D. thesis, Dartmouth College, 2014.