Research

Research Interests

I am broadly interested in combinatorics, algebra, and geometry. More specifically, I am interested in various topics related to:

Dimer Models
Cluster Algebras
Enumerative Combinatorics
Symplectic and Poisson Geometry
Integrable Systems
Teichmüller Theory and Character Varieties

For a more detailed description of my research, you can read my research statement.

Collaborators

Nickolas Anderson	Semeon Artamonov	Etan Basser	Amanda Burcroff	Andrew Claussen
Daniel Douglas	Moriah Elkin	Elizabeth Kelley	Richard Kenyon	John Machacek
Gregg Musiker	Samuel Panitch	Anuj Sakarda	Ralf Schiffler	Michael Shapiro
Sri Tata	Kayla Wright	Sylvester Zhang

Preprints

A Quantum N-Dimer Model
(with Dan Douglas, Richard Kenyon, Sam Panitch, and Sri Tata)
Arxiv:2510.07543

Local Statistics of the M_n Dimer Model
(with Nickolas Anderson, Moriah Elkin, Elizabeth Kelley, and Kayla Wright)
Arxiv:2508.19224

Mixed Dimer Models for Euler and Catalan Numbers
(with Andrew Claussen)
Arxiv:2503.11936

Some Aspects of Higher Continued Fractions
(with Etan Basser and Anuj Sakarda)
Arxiv:2401.12859

Higher Dimer Covers on Snake Graphs
(with Gregg Musiker, Ralf Schiffler, and Sylvester W. Zhang)
Arxiv:2306.14389

Publications

Higher q-Continued Fractions
(with Amanda Burcroff, Ralf Schiffler, and Sylvester W. Zhang)
European Journal of Combinatorics

Eigenvalues of Matrix Products
(with Richard Kenyon)
Bulletin of the London Mathematical Society (2025)
Arxiv:2407.10786

Higher-Rank Dimer Models
(with Richard Kenyon)
Transactions of the American Mathematical Society (2025)
Arxiv:2312.03087

Noncommutative Networks on a Cylinder
(with Semeon Arthamonov and Michael Shapiro)
Communications in Mathematical Physics (2024)
Arxiv:2008.02889

q-Rational and q-Real Binomial Coefficients
(with John Machacek)
Advances in Applied Mathematics (2023)
Arxiv:2301.08185

q-Rationals and Finite Schubert Varieties
Comptes Rendus Mathematique (2023)
Arxiv:2111.07912

Matrix Formulae for Decorated Super Teichmüller Spaces
(with Gregg Musiker and Sylvester Zhang)
Journal of Geometry and Physics (2023)
Arxiv:2208.13664

Double Dimer Covers on Snake Graphs from Super Cluster Expansions
(with Gregg Musiker and Sylvester Zhang)
Journal of Algebra (2022)
Arxiv:2110.06497

Discrete Dynamical Systems From Real Valued Mutation
(with John Machacek)
Experimental Mathematics (2022)
Arxiv:2109.06927

An Expansion Formula for Decorated Super-Teichmüller Spaces
(with Gregg Musiker and Sylvester Zhang)
SIGMA (2021)

Non-Commutative Integrability of the Grassmann Pentagram Map
Advances in Mathematics (2020)
Arxiv:1810.11742

Log-Canonical Coordinates for Poisson Brackets and Rational Changes of Coordinates
(with John Machacek)
Journal of Geometry and Physics (2017)
Arxiv:1703.06521

Slides From Talks

Higher Dimer Covers and Continued Fractions

Cluster Superalgebras from Triangulated Surfaces

Noncommutative Poisson Structures from Networks

q-Rationals and Finite Schubert Varieties