Dr Chris Wendl, PhD
Royal Society University Research Fellow

Room 802A
Tel: ++44 (0)20-7679-2272
E-mail: wendlmath.ucl.ac.uk
Fax: 020-7383-5519

Research Interests
Symplectic and Contact Geometry/Topology

In broad terms, I am interested in geometric and topological problems that can be solved using the technology of analysis -- and conversely, in the analytical intricacies of PDEs that have geometric applications. Thus far my research in this area has been concentrated in the fields of symplectic and contact topology. A symplectic manifold is essentially the natural geometric setting for Hamiltonian mechanics, and contact manifolds can be viewed as a special class of energy hypersurfaces in symplectic manifolds. The theory thus has plenty of applications to dynamical questions, but it has many fascinating connections with other fields as well. Since Gromov's seminal work in 1985, the most powerful technology used in this area has been the theory of pseudoholomorphic curves: these are solutions to an elliptic PDE that generalizes the Cauchy-Riemann equations of complex analysis. By counting solutions to these equations in various settings, one can define a wealth of symplectic and contact invariants that go by names such as Gromov-Witten Theory, Floer Homology, Contact Homology and Symplectic Field Theory. The algebraic structure of these theories is a topic of considerable interest in itself, among other reasons because they have formal similarities to objects that arise naturally in Quantum Field Theory. My most recent work has focused on the application of holomorphic curve techniques to understand when a given contact manifold is or is not symplectically fillable, and which pairs of contact manifolds can be related to each other by symplectic cobordisms.