Research
Broadly, my research interests lie in analyzing and developing mathematical models of phenomena in the physical and biological sciences. As an applied mathematician, I find significant professional satisfaction in studying “toy” models that are simple enough to analyze but rich enough to yield concrete insights into phenomena observed in nature.
I am particularly drawn to problems that have both interesting applications and the potential to lead to new mathematics. My work draws on the calculus of variations, mathematical modeling, applied analysis, continuum mechanics, asymptotic methods, ordinary and partial differential equations, stochastic processes, and Riemannian geometry. A unifying theme is the use of variational and dynamical ideas to understand interdisciplinary problems.
Students interested in working with me may also want to visit the Student Projects page to see examples of past projects. A copy of my research statement can be found here (.pdf).
Selected talks
Selected work
My newest climate work uses large-deviation ideas to determine the most probable route by which weak noise can drive a periodically forced Arctic energy-balance model from a perennial-ice state to an ice-free state.
This work asks how small nongradient perturbations change the geometry of rare escapes. We combine Freidlin–Wentzell theory, a Hamiltonian formulation of the variational problem, and Melnikov theory to determine when the optimal escape path persists as a heteroclinic orbit.
A low-dimensional hurricane model provides a clean setting for comparing bifurcation-, rate-, and noise-induced tipping. The analysis distinguishes mechanisms that destabilize an existing storm from mechanisms capable of activating a storm from the non-storm state.
For stochastic systems with discontinuous drift, standard Freidlin–Wentzell theory must be modified. By smoothing the vector field and passing to the limit with Γ-convergence, we obtain a rate functional that can capture noise-induced sliding and non-unique transition paths.
In collaboration with Gary Moon and Sarah Raynor, we study regularity of two-phase elliptic free-boundary problems on polygonal domains, with particular interest in how interfaces interact with Neumann corner points.
My retinal work uses spherical geometry to explain how local tuning on the curved eye forms global neural codes. The 2017 Nature study identified optic-flow channels aligned with the body and gravitational axes, while the 2025 Cell Reports study found a related spherical code for edge orientation.
With Hannah Scanlon, I studied an SIR network in which susceptible individuals temporarily deactivate connections to infected neighbors. A mean-field approximation reveals how behavioral link changes alter the threshold for epidemic spread.
In work on generalized and inverse-square brachistochrone problems, I have used the calculus of variations, geometric optics, and weak solutions to understand time-minimizing paths in nonuniform gravitational fields.
A sequence of projects on non-Euclidean elasticity studies how swelling, Gaussian curvature, and bending-energy minimization generate periodic and self-similar shapes in thin sheets.
Using variational methods, asymptotics, and phase-retrieval algorithms, I studied how phase modulation can create prescribed axial intensity profiles despite diffraction.