String Theory in particular and quantum field theory in general, with focus on topological strings, mirror symmetry, and supersymmetric theories for which one can obtain non-perturbatively exact results by using methods of algebraic geometry.
More recently I was working on various aspects of the weak gravity conjectures, which constrain the possible quantum field theories that can be consistently coupled to gravity, and on applying methods of algebraic geometry to the AdS3/CFT correspondence.