Abstract :

A pseudoholomorphic curve (or J-holomorphic curve) is a smooth map from A Riemann surface into an almost complex manifold that satisfies Cauchy Riemann equation. J holomorphic curves lead to the Gromov-Witten invariants and Floer homology and plays a prominant role in string theory. In this talk I will define Symplectic manifold and almost complex structure on a manifold then using these I'll discuss what is a pseudoholomorphic curve and its analogy with Cauchy Riemann equations.