I am an Assistant Professor at George Mason University, in the Department of Mathematical Sciences. My research interests are applied, stochastic, and computational geometry and topology, and applications to materials science, physics, and biology.
I am looking for graduate students in the areas of stochastic topology and/or development of methodology for the quantification of materials geometry. Email me if you are interested!
Email: bschwei @ gmu (dot) edu
P. Duncan, M. Kahle, and B. Schweinhart,
Homological Percolation on a Torus: Plaquettes and Permutohedra, (November 2020, revised August 2021).
F. Manin, É. Roldán, and B. Schweinhart, Topology and Local Geometry of the Eden Model, submitted (May 2020).
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B. Schweinhart, Limits of Embedded Graphs, and Universality Conjectures for the Network Flow, (unpublished preprint) June 2017.
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.
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).
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).
Local Feature Classification in Microstructures using the Local Wasserstein Distance, Mini-symposium on on Statistical Descriptors of Materials at Multiple Length Scales, SIAM Conference on Mathematical Aspects of Materials Science, Portland (07/2018).
Persistent Homology and the Upper Box Dimension, Applied Algebraic Topology Research Seminar (April 2018).