Joshua Davis, Lecturing Fellow and Teaching Assistant Professor
Please note: Joshua has left the Mathematics department at Duke University; some info here might not be up to date.  Contact Info:
 Education:
PhD  University of Wisconsin  2005 
BA  Oberlin College  1998 
 Specialties:

Geometry
Topology
 Research Interests: symplectic topology, algebraic geometry, string theory
Loosely speaking, GromovWitten invariants are rational numbers that count how many pseudoholomorphic curves (maps from closed surfaces satisfying certain stringent conditions, including the CauchyRiemann equation) there are in a given symplectic manifold. These invariants are used to gain information and prove results about symplectic manifolds; they also play a crucial role in (type IIA) string theory, a branch of physics that attempts to unify general relativity and quantum mechanics.
My own work concerns the definition of relative GromovWitten invariants in certain singular situations, and how the invariants behave under symplectic surgeries.
 Keywords:
symplectic topology • algebraic geometry • GromovWitten invariants
 Curriculum Vitae
