8. Unified criteria for crystallization in hard-core lattice systems with applications to polyomino fluids and chiral mixtures. [arXiv]
I generalize the criteria in [3] for high-density crystallization in hard-core lattice systems to allow for (a) a general measure of local order and (b) multiple translationally inequivalent particle shapes. As a direct consequence, every polyomino admitting a finite number of tilings (with rotations and possibly mirror images) crystallizes at high densities.
7. Extended regime of nematic order in an interacting monomer-dimer model of Heilmann and Lieb. [arXiv]
I prove that a two-dimensional model for liquid crystals introduced by Heilmann and Lieb (1979) exhibits nematic order over a much larger parameter regime than previously known (Jauslin–Lieb, 2018) by adapting the proof strategy developed by Hadas and Peled (2025) for the 2×2 hard square model.
6. Liquid-vapor transition in a model of a continuum particle system with finite-range modified Kac pair potential; with Ian Jauslin, Joel Lebowitz, and Ron Peled. [arXiv]
We prove that a class of continuous particle systems with mesoscopically tailored, finite-range pair potentials exhibits liquid-vapor transitions by verifying a criterion of Dobrushin and Shlosman (1981).
5. Upper bounds for the connective constant of weighted self-avoiding walks. Journal of Physics A: Mathematical and Theoretical, 2025. [arXiv | journal | GitHub]
Extending an earlier work by Alm (1993), I develop a method for deriving upper bounds on the connective constant of weighted self-avoiding walks, with implications for the convergence of the corresponding anisotropic generating functions. A Python implementation of the method is publicly available.
4. Analyticity for locally stable hard-core gases via recursion. Journal of Statistical Physics, 2025. [arXiv | journal]
Extending the recursion method developed by Michelen and Perkins (2025), I expand the known range of activities for which a continuum system of hard spheres with an additional attractive pair interaction is in the gas phase. In the high-temperature regime, the improvement surpasses the classical Penrose–Ruelle bound by at least a factor of e^2.
3. High-fugacity expansion and crystallization in non-sliding hard-core lattice particle systems without a tiling constraint; with Ian Jauslin. Journal of Statistical Physics, 2024. [arXiv | journal]
We prove that a large class of hard-core lattice particle models crystallize at high densities, using a novel characterization of local order based on discrete Voronoi diagrams.
2. Counting conjugacy classes of elements of finite order in exceptional Lie groups; with Tamar Friedmann. Combinatorial Theory, 2024. (undergraduate research) [arXiv | journal | data]
1. Links, bridge number, and width trees; with Scott Taylor. Journal of the Mathematical Society of Japan, 2023. (undergraduate research) [arXiv | journal]
