**Symplectic
Topology, Geometry, and Gauge Theory Program**
## Coxeter Lecture Series

March 12, 13, 14, 2001, 3:00 - 4:00 p.m.

Article on Lecture

## Alexander B. Givental

Professor of Mathematics,

University of California at Berkeley

California Institute of Technology

M.S., Institute of Oil and Gas Industry (Moscow), 1980

Ph.D., Moscow State University, 1987

*Gromov - Witten invariants in higher genus*

Abstract:

The objective of the series is to introduce a formula expressing enumerative
information about higher genus holomorphic curves in complex projective
spaces (and conjecturally --- in many other complex algebraic manifolds)
in terms of such information in genus zero. The subject intertwines
the Witten-Kontsevich intersection theory on Deligne-Mumford moduli
spaces of Riemann surfaces and axiomatic 2-dimensional topological fields
theory with elementary representation theory of loop groups.