Research

Publications and Pre-Prints

  1. Calibrated representations of the double Dyck path algebra-  with E. Gorsky and J. Simental. https://arxiv.org/pdf/2311.17653.pdf
  2. Triangular (q,t)-Schröder Polynomials and Khovanov-Rozansky Homology- with C. Caprau, M. Hogancamp, and M. Mazin (submitted) 
  3. Mesas of Stirling permutations - with P. Harris, G. Kirby, M. Vega, and B. Tenner - https://arxiv.org/abs/2306.12158
  4. Higher rank (q,t)-Catalan polynomials, Affine Springer Fibers, and a Finite Rational Shuffle Theorem - with J.  Simental and M. Vazirani - Transactions of the AMS (to appear) - https://arxiv.org/abs/2303.15694
  5. Extremal tensor products of Demazure crystals are direct sums of Demazure crystals- with S. Assaf and A. Dranowski, ,Séminaire Lotharingien de Combinatoire 89B (2023), Article #12
  6. Semi-standard parking functions and a finite Shuffle theorem - with J.  Simental and M. Vazirani , Séminaire Lotharingien de Combinatoire  89B (2023), Article #84
  7. Pinnacle sets of signed permutations - with P. Harris, G. Kirby, M. Vega, and B. Tenner - Discrete Math, Vol 346, Issue 7, July 2023,  
  8. Extremal tensor products of Demazure crystals - with S. Assaf and A. Dranowski - Algebras and Representation Theory (2023)
  9. On Khovanov homology and related invariants  - joint with C. Caprau, C. Lee, A. Lowrance, R. Sazdanovic, M. Zhang. - Research Directions in Symplectic and Contact Geometry and Topology, AWMS vol 27. Springer 
  10. Affine Demazure crystals for specialized nonsymmetric Macdonald polynomials - joint with Sami Assaf, Algebraic Combinatorics  https://arxiv.org/abs/2002.04141
  11. Demazure Crystals for specialized nonsymmetric Macdonald polynomials -joint with Sami Assaf Journal of Combinatorial Theory-Series A Vol 182 (2021)   -  https://arxiv.org/abs/1901.07520
  12. Categorical Bernstein 0perators and the Boson-Fermion correspondence ,  Selecta Mathematica 26, Article number: 51 (2020) -https://arxiv.org/abs/1808.01235.
  13.  Crystal graphs, key tabloids, and nonsymmetric Macdonald polynomials, Séminaire Lotharingien de Combinatoire, 80B (2018) Article #81, 12pp.- joint with Sami Assaf. 

Other

14. Chapters 8-9 in Introduction to Soergel bimodules, - joint with Ben Elias. RSME Springer Series on the 2017 MSRI graduate school on Soergel bimodules.

Dissertation

15. Categorical Operators and Crystal Structures on the Ring of Symmetric Functions - available through the USC digital library here.

Posters I have previously presented: 

1. Categorical Bernstein operators and the Boson-Fermion correspondence  here
2. Crystals, Keys, and nonsymmetric Macdonald polynomials  here

Collaborators