My advisor is Max Engelstein. Currently, I am working on a project investigating bounds of the Green's Functions of Elliptic PDE with Robin boundary conditions. In particular, I am looking at the 2-dimensional analog of work of David, Decio, Engelstein, Filoche, Mayboroda, and Michetti.
I am also interested in research questions that involve the David-Semmes problem and creating examples of Calderón-Zygmund operators which are L^2 bounded on purely unrectifiable sets in R^n, as well as connecting qualitative conditions on singular integral operators to quantitative counterparts.