Interests

Geometric measure theory, variational problems, interface evolution models, curvature flows, geometric optimization, geometric analysis, convexity, inequalities, image analysis.

My research is primarily in geometric measure theory and the calculus of variations. It includes work on convexity, lower semicontinuity of energies, existence of energy minimizers, and boundary regularity, for static optimization problems as well as geometric evolution problems, often in the setting of partitions of Euclidean space. I have worked on curvature flows, isoperimetric problems, geometric optimization, total variation minimization, and probability inequalities. I am interested in applications to various fields, such as materials science, image processing, and medicine.

Academic Appointment(s)

Primary

Associate Professor, Department of Mathematics and Statistics