I have a broad range of mathematical interests, but my current research focus is primarily in spectral geometry. Most of the work of my PhD was on Rauch's hot spots conjectures under various boundary conditions and in several geometric settings. I am also interested in the problem of comparing Dirichlet and Neumann Laplace eigenvalues. Other ongoing projects include studying curl eigenvalues on three-dimensional domains and Laplace eigenvalues of hyperbolic surfaces.
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.
Publications
A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region. Journal of Spectral Theory, 2025. (ArXiv)
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.