Research Papers
Critical Point Theory and Finite Topological Type under Nonnegative Weighted Sectional Curvature
In Preparation
Modified Hessian Comparison and Excess Estimates on Manifolds with Density
In Preparation
Comparison Geometry on Manifolds with Density via Modified Hessians
Submitted (2026). arXiv:2605.24407
On homogeneous closed gradient Laplacian solitons
Differential Geometry and its Applications 93, (2024). arXiv:2302.11441
On homogeneous closed gradient Laplacian solitons and the modified conformal Hessian
Syracuse University Ph.D. Thesis (2023).
Research Interests
My research interests are in differential geometry and geometric analysis. I am broadly interested in weighted curvature of manifolds with density and solitons of geometric flows. Recently, I am interested in the geometric consequences of a modified Hessian tensor arising from the framework of Kennard-Wylie-Yeroshkin for studying manifolds with density.
Upcoming Talks
"On homogeneous closed gradient Laplacian solitons", Informal Geometric Analysis Seminar - Northwestern University, October 26, 2023
"Homogeneous Closed Gradient Laplacian Solitons", Joint Mathematics Meeting, AMS Special Session on New Developments in Differential Geometry and Topology - Boston, Massachusetts, January 5, 2023
"Normed Divison Algebras, Vector Cross Products, and G_2-Structures", MGO Colloquium - Syracuse University, October 20, 2022
"Homogeneous Closed Gradient Laplacian Solitons", Geometry and Topology Seminar - Syracuse University, October 7, 2022