Algebraic and Complex Geometry and their
interaction with Mathematical Physics. I am particularly interested in
moduli theory, especially stable morphisms and Gromov-Witten invariants,
and stable sheaves and Donaldson-type invariants.
Specifically, I have worked on the moduli spaces of
stable maps to flag varieties, their tautological rings and divisor
theory; on
the intersection theory of Quot schemes on curves; on the intersection
theory of moduli spaces of bundles over curves; on level-rank dualities of
spaces of generalized theta functions; on moduli spaces of sheaves on
surfaces, with connections to abelian varieties and holomorphic symplectic
manifolds.
