I study Riemannian geometry, or, more specifically, I study the flexibility of positive curvature conditions, though my work has been primarily in constructing examples of metrics of positive Ricci curvature. I am also very interested in smooth topology and its relationship to positive curvature.
The space of positive Ricci curvature metrics on spin manifolds, 2020. ArXiv e-print. 23 pages.
Metrics of positive Ricci curvature on the connected sums of products with arbitrarily many spheres, 2020. Annals of Global Analysis and Geometry. 44 pages.
Metrics of Positive Ricci Curvature on Connected Sums: Projective Spaces, Products, and Plumbings, 2019. PhD Thesis. 236 pages.
Ricci-positive metrics on connected sums of projective spaces, 2019. Differential Geometry and its Applications, Volume 62, pages 212–233, 2019.
A simplicial Tutte“5”-flow conjecture, 2014. ArXiv e-prints. 26 pages.
On the Tutte-Krushkal-Renardy polynomial for cell complexes, 2014. Journal of Combinatorial Theory, Series A, Volume 123, Issue 1, Pages 186-201. With Carlos Bajo and Sergie Chmutov.
Generic Polynomials for Transitive Permutation Groups of Degree 8 and 9, 2013. Rose-Hulman Institute of Technology Undergraduate Math Journal, Volume 13, Issue 1, Web. 21 pages. With Jonathan Jonker.