Research Interests

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

Collaborators

• Semeon Artamonov
• Etan Basser
• Amanda Burcroff
• Richard Kenyon
• John Machacek
• Gregg Musiker
• Anuj Sakarda
• Ralf Schiffler
• Michael Shapiro
• Sylvester Zhang

Preprints

• Higher q-Continued Fractions
  (with Amanda Burcroff, Ralf Schiffler, and Sylvester W. Zhang)
  Arxiv:2408.06902


• Eigenvalues of Matrix Products
  (with Richard Kenyon)
  Arxiv:2407.10786


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


• Higher-Rank Dimer Models
  (with Richard Kenyon)
  Arxiv:2312.03087


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

Publications

• Noncommutative Networks on a Cylinder
  (with Semeon Arthamonov and Michael Shapiro)
  Communications in Mathematical Physics
  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, Volume 17 (2021)


• Non-Commutative Integrability of the Grassmann Pentagram Map
  Advances in Mathematics, Volume 373, October 2020
  Arxiv:1810.11742


• Log-Canonical Coordinates for Poisson Brackets and Rational Changes of Coordinates
  (with John Machacek)
  Journal of Geometry and Physics, Vol 121 (2017)
  Arxiv:1703.06521

Slides From Recent Talks

• Higher Dimer Covers and Continued Fractions


• Cluster Superalgebras from Triangulated Surfaces


• Noncommutative Poisson Structures from Networks


• q-Rationals and Finite Schubert Varieties