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:
|PhD||University of Wisconsin||2005|
- 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.
- symplectic topology • algebraic geometry • Gromov-Witten invariants
- Curriculum Vitae