
Almost Complex Structures, GromovWitten Invariants and
Quantum Cohomology
Eaman Eftekhary,
Department of Mathematics,
Princeton, USA

Abstract:
The existance of quantum ring structure was first suggested by C. Vafa
in 1990. Later on, it was reformulated by E. Witten and rigorously proved
by Y. Ruan and G. Tian and later by other people.
The crutial step is the construction of GromovWitten invariants for
Kahler (or more generally symplectic) manifolds. These are certain counts
of pseudoholomomorphic curves inside the given manifold X (for a generic
almost complex structure J on the tangent bundle TX of X) satisfying some
fixed combinatorial conditions.
I will sketch the main ideas in the construction of GWinvariants,
and their relevance to the construction of quantum cup product. Then I
will try to present the new ideas/directions in constructing refined
versions of GWinvariants. All these constructions are motivated by a
conjecture of R. Gopakumar and C. Vafa which relates the BPSstates with
the GWinvariants.

Information:
Date: Sunday & Tuesday, June 1 & 3, 2003, 15:0017:00
Place: School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran

See some photos.

 
