There are three individual researchers supported on this grant. Professor Freed and various coauthors study first twisted K-theory and loop groups, secondly differential K-theory and geometric invariants of Dirac operators, and finally anomalies in M-theory and string theory. Professor Hausel researches new mathematics in quaternionic geometry which corresponds to known mathematics in complex geometry, such as the moduli space of Higgs bundles, square integrable harmonic forms, integration on circle compact manifolds and face vectors of hyperplane arrangements. Professor Uhlenbeck has two projects on hyperbolic equations, one of finding fundamental solutions of covariant-derivative wave operators and one studying wave map blow-up in two space dimensions. She also studies Virasoro actions in TCFT.
The three supported researchers are part of a large geometry group whose research projects span many topics in geometry which originate in high energy theoretical physics or engineering physics. In mathematics proper the work of the group is not limited to geometric analysis, but also involves algebraic geometry, geometric topology, algebraic topology, representation theory, harmonic analysis, and mathematical physics. Essential to the group research are collaborations among mathematicians with diverse backgrounds in mathematics, physics and biology.
