I have a broad range of mathematical interests, but my current research focus is on spectral geometry. In particular, I am currently working on some problems related to the hot spots conjecture of J. Rauch, which states that given a generic initial heat distribution on some object, the hottest and coldest points will tend toward the boundary as time progresses. I have more recently begun to think about questions pertaining to the relationship between the Dirichlet and Neumann Laplace spectra on Euclidean domains and Riemannian manifolds.
My publications and pre-prints can be found below or on Google scholar.
Pre-prints
Hot spots in cones and warped product manifolds. ArXiv:2508.18054, 2025.
Hot spots in domains of constant curvature. ArXiv:2508.13353, 2025.
Geometric inequalities between Dirichlet and Neumann eigenvalues. ArXiv:2504.18517, 2025.
To appear
A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region. To appear in Journal of Spectral Theory, 2025.
Publications
The hot spots conjecture for some non-convex polygons. SIAM Journal of Math. Analysis, 2025. (ArXiv)
First mixed Laplace eigenfunctions with no hot spots. Proc. of AMS, 2024. (ArXiv)
Alternative SIAR models for infectious diseases and applications in the study of non-compliance, with Marcelo Bongarti, Luke Diego Galvan, Michael R. Lindstrom, Christian Parkinson, Chuntian Wang, and Andrea Bertozzi. Mathematical Models and Methods in Applied Sciences, 32(10), 2022, pp. 1987-2015.