Research

Papers and preprints.

M. Shea, "Split Two-Periodic Aztec Diamond," Ann. Henri Poincaré (2026). https://doi.org/10.1007/s00023-026-01675-2 (arXiv: https://arxiv.org/abs/2502.18349)

M. Shea, "Dimer model on the square lattice with interface," arXiv:2202.04210 (2022).

M. Shea, "Generalized Gelfand-Yaglom formula for a discretized quantum mechanic system," J. Math. Phys. 62, (2021). https://doi.org/10.1063/5.0059030

Research interests. 

Broadly I am interested in mathematic problems inspired by physics, in particular quantum and statistical mechanics, and I use methods from combinatorics, probability, and geometry to solve these problems. Of late, I have been studying the scaling limit of certain two-dimensional dimer models.