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Background
Research Interests
- Manifold Learning | Diffusion Maps | Applied Differential Geometry and Topology | Mesh-Free Methods in PDE | Discrete and Finite Element Exterior Calculus | Numerical Analysis
Publications and Preprints
- R. Vaughn, T. Berry and H. Antil, Diffusion Maps for Embedded Manifolds with Boundary with Applications to PDEs. Preprint, 2019.
- O. Babb, A. Malhotra, R. Vaughn, Y. Ayub, and T. Berry, Minimum Curvature Embeddings for Dimensionality Reduction. In Preparation, 17 pages, 2019.
- K.Mellinger, R. Vaughn, and O. Vega, Graphs Embedded into Finite Projective Planes. Contributions to Discrete Mathematics. 2015.
Presentations
- (Upcoming Invited Talk) May 2020: A Data-Driven Approach to Solving Boundary Value Problems with Diffusion Maps. SIAM Conference on the Mathematics of Data Scinece, Cincinnati, OH.
- March 2019: Student Research Talks, GMU. The Hodge Decomposition Theorem.
- September 2018: Student Research Talks, GMU. Kernel Methods in Dimensionality Reduction.
- September 2016: Student Research Talks, GMU. What is Persistent Homology?