Research
Publications and Pre-Prints
Publications and Pre-Prints
- Calibrated representations of the double Dyck path algebra- with E. Gorsky and J. Simental. https://arxiv.org/pdf/2311.17653.pdf
- Triangular (q,t)-Schröder Polynomials and Khovanov-Rozansky Homology- with C. Caprau, M. Hogancamp, and M. Mazin (submitted)
- Mesas of Stirling permutations - with P. Harris, G. Kirby, M. Vega, and B. Tenner - https://arxiv.org/abs/2306.12158
- 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
- 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
- Semi-standard parking functions and a finite Shuffle theorem - with J. Simental and M. Vazirani , Séminaire Lotharingien de Combinatoire 89B (2023), Article #84
- Pinnacle sets of signed permutations - with P. Harris, G. Kirby, M. Vega, and B. Tenner - Discrete Math, Vol 346, Issue 7, July 2023,
- Extremal tensor products of Demazure crystals - with S. Assaf and A. Dranowski - Algebras and Representation Theory (2023)
- 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
- Affine Demazure crystals for specialized nonsymmetric Macdonald polynomials - joint with Sami Assaf, Algebraic Combinatorics https://arxiv.org/abs/2002.04141
- 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
- Categorical Bernstein 0perators and the Boson-Fermion correspondence , Selecta Mathematica 26, Article number: 51 (2020) -https://arxiv.org/abs/1808.01235.
- 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 here2. Crystals, Keys, and nonsymmetric Macdonald polynomials here
Collaborators