Ph. D., Stanford University, 2016
BSc, University of Edinburgh, 2012
Analysis and Partial Differential Equations, Differential Geometry
Differential Geometry & PDE's
I study problems in geometric analysis and geometric measure theory. I am particularly interested in the regularity of minimal surfaces and mean curvature flow. Minimal surfaces are mathematical models of static soap films, and like their real-world analogues will not in general be smooth. A lot of my research studies the behavior of minimal surfaces near their singularities, and the structure of the singular set itself.
- Effective Reifenberg theorems in Hilbert and Banach spaces (w/ Aaron Naber and Daniele Valtorta). To appear in Math. Ann. (2018).
- The singular set of minimal surfaces near polyhedral cones (w/ Maria Colombo and Luca Spolaor). Submitted (2017).
- Quantitative stratification for some free-boundary problems (w/ Max Engelstein). To appear in Trans. Amer. Math. Soc. (2017).
- Quantitative Reifenberg theorem for measures (w/ Aaron Naber and Daniele Valtorta). Submitted (2016).
- The free-boundary Brakke flow. To appear in J. Reine Angew. Math. (2017).