Research

Papers and preprints

• Limit shapes for domain-wall (colored) vertex models, with P.d. Francesco, preprint, 2025.
• Diffusive scaling limit of stochastic Box-Ball systems and PushTASEP, with M. Kim, E. Loeser, and H. Lyu, preprint, 2025.
• Perfect t-embeddings of uniformly weighted generalized tower graphs, with H.T. Vu, preprint, 2025.
• Colored vertex models and interacting reverse plane partitions, with J. Guse and D. Jiang, preprint, 2025.
• Edge universality of beta-additions through Dunkl operators, with J. Xu, submitted for publication, 2024.
• Asymptotics of Bounded Lecture-Hall Tableaux, with Z. Li and I. Prause, submitted for publication, 2024.
• Shuffling algorithm for coupled tilings of the Aztec diamond, with M. Nicoletti, Annales Henri Poincaré, vol. 25, no. 12, pp. 5187-5229. Cham: Springer International Publishing, 2024.
• Colored vertex models and k-tilings of the Aztec diamond, with S. Corteel and A. Gitlin, Transactions of the AMS, accepted.
• A vertex model for supersymmetric LLT polynomials, with A. Gitlin, Annales de l’Institut Henri Poincaré D 11, no. 3 (2023): 571-640.
• Equivalences of LLT polynomials via lattice paths, Combinatorial Theory, accepted.
• A vertex model for LLT polynomials, with S. Corteel, A. Gitlin, and J. Meza, International Mathematics Research Notices 2022, no. 20 (2022): 15869-15931.
• Area statistics of large oscillating tableaux, preprint, 2020.
• Integrability of limit shapes of the inhomogeneous six vertex model, with N. Reshetikhin and A. Sridhar, Communications in Mathematical Physics 391, no. 3 (2022): 1181-1207.
• Arctic curves phenomena for bounded lecture hall tableaux, with S. Corteel and M. Nicoletti, Communications in Mathematical Physics 382, no. 3 (2021): 1449-1493.
• Conformal limit for dimer models on the hexagonal lattice, with N. Reshetikhin and A. Sridhar, Journal of Mathematical Sciences 242, no. 5 (2019).
• Random tilings with the GPU, with A. Sridhar, Journal of Mathematical Physics 59, no. 9 (2018).
• Validation and benchmarking of two particle-in-cell codes for a glow discharge, with J. Carlsson, et al., Plasma Sources Science and Technology 26, no. 1 (2016): 014003.
• Deterministic domain wall motion orthogonal to current flow due to spin orbit torque, with D. Bhowmik, et al., Scientific Reports 5, no. 1 (2015): 11823.

Talks

• A vertex model for LLT polynomials, UIUC Integrability and Representation Theory Seminar, UIUC, September 2024.
• Vertex models, symmetric polynomials, and tilings, UIUC Algebra-Geometry-Combinatorics seminar, UIUC, September 2024.
• The stochastic box-ball system, Geometry, Statistical Mechanics, and Integrability Workshop IV: Vertex Models: Algebraic and Probabilistic Aspects of Universality, Institute for Pure and Applied Mathematics, May 2024.
• Coupled Tilings of the Aztec diamond, JMM Special Session on Solvable Lattice and their Applications, January 2024.
• Coupled tilings of the Aztec diamond, Mathematical Physics Seminar, Purdue University, November 2023.
• Coupled tilings, double dimers, and LLT polynomials, Integrable Probability Seminar, MIT, October 2023.
• Double dimers, coupled tilings, and LLT polynomials, DIMERS Closing Conference, Sorbonne Université, July 2023.
• k-tilings of the Aztec Diamond, Berkeley Probability Seminar, UC Berkeley, April 2023.
• k-tilings of the Aztec Diamond, Journées Cartes, Institute of Theoretical Physics, June 2022.
• k-tilings of the Aztec Diamond, Enumerative and Analytic Combinatorics Seminar, Université Paris Cité, June 2022.
• Lattice models and LLT polynomials, Madison Combinatorics Seminar, UW Madison, May 2022.
• k-tilings of the Aztec Diamond, Madison Probability Seminar, UW Madison, April 2022.
• k-tilings of the Aztec Diamond, Solvable lattice model seminar, Stanford University, February 2022.
• A Vertex Model for LLT Polynomials, Berkeley Combinatorics Seminar, UC Berkeley, December 2020.
• A Vertex Model for LLT Polynomials, CMS Winter Meeting, December 2020.
• Arctic Curves, Lecture Hall Tableaux, and the Tangent Method, LPSM Friday Seminar, Sorbonne University, November 2019.
• Arctic Curves, Lecture Hall Tableaux, and the Tangent Method, Berkeley Combinatorics Seminar, UC Berkeley, September 2019.
• Arctic Curves in Lecture Hall Tableaux, Asymptotic Algebraic Combinatorics Workshop, Banff International Research Station, March 2019.
• Random Tilings with the GPU, Representation Theory, Mathematical Physics and Integrable Systems, Centre International de Rencontres Mathmatiques, June 2018.

Organization

• I coorganized the 2025 SLMath summer school "Graphical Models in Algebriac Combinatorics."
• I coorganize the UIUC Algebra-Geometry-Combinatorics seminar: Fall 2024, Spring 2025, Fall 2025
• I coorganize the UIUC Integrability and Representation Theory seminar: Fall 2024 and Spring 2025
• I coorganized the UW Madison Probability seminar.

Slides

Some slides from my talks:

• Random tilings on the gpu
• Arctic curves for bounded lecture hall tableaux
• Coupled tilings of the Aztec diamond