Method of pseudoholomorphic curves and applications (Part 3)

Appears in collection : Summer School 2012 - FEUILLETAGES, COURBES PSEUDOHOLOMORPHES, APPLICATIONS

The method of « pseudoholomorphic » curves proved itself to be extremely useful in different fields. In symplectic topology, for instance Gromov’s Nonsqueezing Theorem, Arnold’s conjecture and the Floer homology, the Gromov-Witten invariants. In complex analysis and geometry, for instane polynomial hulls of totally real surfaces, envelopes of meromorphy, holomorphic foliations. We shall develop the theory of complex curves in almost complex manifolds and discuss some of these applications in our lectures.