Faculty & Staff Directory
Benjamin Schweinhart
- Assistant Professor
Contact Info
- Name
- Benjamin D. Schweinhart
- Job Title
- Assistant Professor
- Website
- Office Number
- Exploratory Hall, Room 2212, MSN 3F2
Affiliations
Departments
- Mathematical Sciences Department (Faculty)
Research Areas
- Applied Mathematics
- Computational Methods
- Data Sciences
- Manifolds and Cell Complexes
- Materials Science
- Mathematics, Artificial Intelligence, and Machine Learning
- Probability
- Topology
Education
PhD, Mathematics, Princeton University (2015)
MA, Mathematics, Princeton University (2011)
BA, Mathematics, Swarthmore College (2009)
About
I am an Assistant Professor in the Department of Mathematical Sciences at George Mason University. My research program focuses on problems in applied, stochastic, and computational geometry and topology, with applications to materials science, physics, and biology. In particular, I study methods to quantify the local geometry and topology of complex geometric structures. Broadly speaking, this work falls under the purview of topological and geometric data analysis, and aspects of it are related to probability, metric geometry, probabilistic combinatorics, network theory, and mathematical physics.
Current Research
My research program focuses on problems in applied, stochastic, and computational geometry and topology, with applications to materials science, physics, and biology. In particular, I study methods to quantify the local geometry and topology of complex geometric structures. Broadly speaking, this work falls under the purview of topological and geometric data analysis, and aspects of it are related to probability, metric geometry, probabilistic combinatorics, network theory, and mathematical physics. Current research topics include (but are not limited to): (1) Materials microstructure quantification and machine learning (joint with T. Berry at GMU and J. K. Mason at UC Davis) (2) Percolation and Topology (joint work with P. Duncan and M. Kahle at Ohio State) (3) Emergent Topology of Random Growth Models (joint work with E. Roldan at TU Munich and D. Sivakoff at Ohio State) (4) Persistent Homology, Machine Learning, and Fractal Dimension (joint work with J. Jaquette at Boston University)
Teaching Focus
I teach a wide range of undergraduate and graduate courses on subjects including topology and probability, as well as service courses such as linear algebra and calculus; more specialized topics include topological and geometric data analysis and stochastic topology.
Selected Publications
B. Schweinhart, Fractal Dimension and the Persistent Homology of Random Geometric Complexes, Advances in Mathematics 372 (2020) https://www.sciencedirect.com/science/article/abs/pii/S0001870820303170
B. Schweinhart, D. Rodney, and J. K. Mason, Statistical Topology of Bond Networks with Applications to Silica, Physical Review 101 (2020) https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.052312
J. Jaquette and B. Schweinhart,Fractal Dimension Estimation with Persistent Homology: A Comparative Study, Communications in Nonlinear Science and Numerical Simulation 84 (2020) https://www.sciencedirect.com/science/article/abs/pii/S1007570419304824 B.
Schweinhart, Persistent Homology and the Upper Box Dimension, Discrete and Computational Geometry (2019). https://link.springer.com/article/10.1007/s00454-019-00145-3
B. Schweinhart, J. K. Mason, and R. D. MacPherson, Topological Similarity of Random Cell Complexes and Applications, Physical Review E 93 (2016). https://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.062111
Awards
NSF Mathematical Sciences Postdoctoral Research Fellowship (2016-2019)
NSF Graduate Research Fellowship (2012-2015)
Centennial Fellowship, Princeton University (2010-2013)
Contact Info
- Name
- Benjamin D. Schweinhart
- Job Title
- Assistant Professor
- Website
- Office Number
- Exploratory Hall, Room 2212, MSN 3F2