About Me

I am a 4th year PhD student in the math department at MIT, working with Larry Guth. My research interests are broadly in geometry and topology, but especially in quantitative topology. My current focus is on studying the Lipschitz homotopy groups of the Heisenberg groups, and on quantitative versions of Gromov's h-principle.


Quantitative nullhomotopy and the Hopf Invariant
I give a quantitative version of a theorem of Hajlasz-Schikorra-Tyson, showing that any extension of a map with nonzero Hopf invariant with small (2n+1)-dilation must have large 2n-dilation. This simplifies their result that Lipschitz null-homotopy cannot have low rank almost everywhere. I show this theorem is sharp by construction extensions withh small (2n+1)-dilation
Slope Gap Distributions of Veech Surfaces (Joint with Jane Wang)
We prove that for a Veech translation surface, the slope gap distribution is piecewise real-analytic with finitely many points of non-analyticity. Submitted for publication.
Removal of Singularites for Stein Manifolds
My undergraduate honors thesis, I gave the full details and extended a result of Gromov and Eliashberg, establishing an h-principle for holomorphic vector bundles over Stein manifolds.