Benjamin Schweinhart

I am an Assistant Professor at George Mason University, in the Department of Mathematical Sciences. My research interests are stochastic, applied, and computational geometry and topology, and applications to percolation theory, materials science, statistical physics, and biology.

Contact Info

Email: bschwei @ gmu (dot) edu

Curriculum Vitae

Papers

P. Duncan and B. Schweinhart, A Sharp Deconfinement Transition for Potts Lattice Gauge Theory in Codimension Two, Communications in Mathematical Physics (2025).


P. Duncan and B. Schweinhart, Topological Phases in the Plaquette Random-Cluster Model and Potts Lattice Gauge Theory, Communications in Mathematical Physics (2025).


S. Eldridge and B. Schweinhart, Hadwiger Models: Low-Temperature Behavior in a Natural Extension of the Ising Model (2024).


D. Miley, E. Suwandi, B. Schweinhart, and J. K. Mason, A Metric on the Polycrystalline Microstructure State Space (2024).


P. Duncan and B. Schweinhart, Some Properties of the Plaquette Random Cluster Model (2024).


P. Duncan, M. Kahle, and B. Schweinhart, Homological Percolation on a Torus: Plaquettes and Permutohedra, to appear in AIHP (2024).


F. Manin, É. Roldán, and B. Schweinhart, Topology and Local Geometry of the Eden Model, Discrete and Computational Geometry (2023).


B. Schweinhart, D. Rodney, and J. K. Mason, Statistical Topology of Bond Networks with Applications to Silica, Physical Review E 101 (2020).


J. Jaquette and B. Schweinhart, Fractal Dimension Estimation with Persistent Homology: A Comparative Study, Communications in Nonlinear Science and Numerical Simulation 84 (2020).


B. Schweinhart, Fractal Dimension and the Persistent Homology of Random Geometric Complexes, 372 Advances in Mathematics (2020).


B. Schweinhart, Weighted Persistent Homology Sums of Random Cech Complexes , July 2018. (Note: this manuscript was largely subsumed into the one above.)


B. Schweinhart, Persistent Homology and the Upper Box Dimension, Discrete and Computational Geometry (2019).


B. Schweinhart, J. K. Mason, and R. D. MacPherson, Topological Similarity of Random Cell Complexes and Applications, Physical Review E 93 (2016), doi: 10.1103/PhysRevE.93.062111.


K. Emmett, B. Schweinhart, and R. Rabadan, Multiscale Topology of Chromatin Folding, Proceedings of the 9th International Conference on Bio-inspired Information and Communications Technologies (2015).


B. Schweinhart, Statistical Topology of Embedded Graphs. , Thesis, August 2015


R. D. MacPherson and B. Schweinhart, Measuring Shape with Topology, Journal of Mathematical Pshysics 53 (2012), doi: 10.1063/1.4737391.

Software

Swatches: Local Structure Classification in Graphs. This software implements the methodology described in "Statistical Topology of Bond Networks with Applications to Silica" and "Topological Similarity of Random Cell Complexes and Applications."


Dimension Estimation with PH0. This software implements the methodology described in "Fractal Dimension Estimation with Persistent Homology: A Comparative Study," and includes C++ code to compute the PH0 dimensionand MATLAB code to compute the correlation dimension (written by J. Jaquette).

Talks with Video/Slides

A Cellular Representation of Potts Lattice Gauge Theory, University of Maryland (05/2025).


The Plaquette Random Cluster Model and Potts Lattice Gauge Theory, IPAM (May 2024).


Plaquette Percolation on the Torus, Percolation Today (February 2021).


Topology and Geometry of Complex Systems, University at Albany (01/2020).


Local Atomic Environments in Oxide Glass, Workshop: Structure in the Micro-world, The Ohio State University (05/2019).


The Persistent Homology of Random Geometric Complexes on Fractals, Conference on Geometric Data Analysis, The University of Chicago (05/2019).