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:

Office Location:	033 Physics Bldg
Office Phone:	(919)-660-2823
Email Address:
Web Page:	http://www.math.duke.edu/~jdavis/

Education:

PhD	University of Wisconsin	2005
BA	Oberlin College	1998

Specialties:

Geometry
Topology

Research Interests: symplectic topology, algebraic geometry, string theory

Loosely speaking, Gromov-Witten invariants are rational numbers that count how many pseudoholomorphic curves (maps from closed surfaces satisfying certain stringent conditions, including the Cauchy-Riemann 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 Gromov-Witten invariants in certain singular situations, and how the invariants behave under symplectic surgeries.

Keywords:

symplectic topology • algebraic geometry • Gromov-Witten invariants

Curriculum Vitae