I am interested in topics in supergeometry, algebraic geometry, and representation theory related to string theory and other ideas in mathematical physics. One of the most interesting topics I work with is the moduli space of super Riemann surfaces, which has special importance in super string theory. This space has many analogous properties to the moduli space of classical Riemann surfaces, but complications arise due to its superstack structure.

The other geometrical space I am interested in is the (super) Sato grassmannian, and especially its relationship with the moduli space of (super) curves. This super grassmannian space despite being infinite dimensional and a superscheme, is a well-studied and "nice" space. It is the geometrical foundation behind τ functions and KP hierarchy studied in integrable systems. Various super generalizations of these ideas have been discussed, but need further development.