# Research

I work in convex geometry. I am interested in the existence and uniqueness of solutions to a variety of Monge-Ampère type equations that come from the study of convex bodies. Solutions to these PDEs lead to the reconstruction of convex bodies when different types of geometric measures are prescribed. In convex geometry, they are known as Minkowski-type problems.

The techniques I use include calculus of variation, geometric flow, method of continuity, and degree theory.

I am also interested in sharp isoperimetric inequalities (both affine and non-affine, geometric and functional).