My research is in the area geometric measure theory or GMT. I also enjoy functional analysis, differential geometry, and partial differential equations.
Below is a unit cube with water in it. The cube can hold one unit of water, and it has twelve edges, each of unit length. We can (and do) ask the question if there exists a polyhedral region that will hold one unit of water while having the least amount of edge length. To learn more, read my research statement.