Faculty Profile

Research Overview:

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:

1. 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.
2. Effective low energy supergravity theories in string compactification and the computation of nonperturbative stringy effects in effective supergravities.
3. D-branes on Calabi-Yau manifolds and BPS state counting. Relations to Borcherds products, automorphic forms, black-hole entropy, and wall-crossing.
4. Applications of the theory of automorphic forms to conformal field theory, string compactification, black hole entropy counting, and the AdS/CFT correspondence.
5. 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.
6. Conformal field theories. Rational conformal field theories, especially applications to the theory of anyons and nonabelions.
7. Topological field theories, and applications to invariants of manifolds.
8. String field theory.
9. String cosmology and time-dependence in string theory
10. Does the alleged landscape of N=1 effective four-dimensional string vacua'' really exist?

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