My work focuses on mathematical physics, with an emphasis on string theory, M-theory, and gauge theories more generally. My work places particular emphasis on the underlying mathematical structures and applications to and from modern mathematics. Specific research interests include:
- The theory of branes and generalized abelian gauge theories in supergravity. This involves interesting topological issues related to generalized differential cohomology theories, especially K-theory. There are also interesting relations to the theory of self-dual fields, anomaly cancellation, and noncommutative geometry.
- Effective low energy supergravity theories in string compactification and the computation of nonperturbative stringy effects in effective supergravities.
- D-branes on Calabi-Yau manifolds and BPS state counting. Relations to Borcherds products, automorphic forms, black-hole entropy, and wall-crossing.
- Applications of the theory of automorphic forms to conformal field theory, string compactification, black hole entropy counting, and the AdS/CFT correspondence.
- Potential connections to number theory. For example - I pointed out in 1998 that the attractor mechanism of supersymmetric black holes singles out Calabi-Yau varieties with relations to complex multiplication.
- Conformal field theories. Rational conformal field theories, especially applications to the theory of anyons and nonabelions.
- Topological field theories, and applications to invariants of manifolds.
- String field theory.
- String cosmology and time-dependence in string theory
- Does the alleged ``landscape of N=1 effective four-dimensional string vacua'' really exist?