B.A., Cambridge University, 1992
Ph.D., Stanford University, 1997
Analysis and Partial Differential Equations, Differential Geometry
I am interested in complex and symplectic geometry. A focus for research is the tangent bundles of real-analytic Riemannian manifolds. These carry canonical complex and symplectic structures. The complex geometry is related to properties of the Riemannian metric and the symplectic geometry to the smooth structure on the underlying manifold. Past research has shown that the map from compact Riemannian to complex (Stein) manifolds is essentially injective. It is an open question whether the same is true for the map from smooth to symplectic manifolds. An important tool in attacking these and other problems is the theory of pseudoholomorphic curves in symplectic manifolds.
- Lagrangian spheres in S^2 x S^2, Geom. Funct. Anal., 14 (2004), 303-318.
- (with D. Burns and S. Halverscheid) The geometry of Grauert tubes and complexification of symmetric spaces, Duke Math. J., 118 (2003), 465-491.
- Stein fillings of lens spaces, Commun. Contemp. Math., 5 (2003), 967-982.
- Antiholomorphic involutions on Stein manifolds, Intern. J. Math., 14 (2003), 479-487.
- Lagrangian unknottedness in Stein surfaces, preprint.