The problems to be studied are among the kernel problems of symplectic topology. The topics include: Classification of contact structures and, especially, fillable contact structures on 3-manifolds; influence of the topology of a pseudoconvex (or contact type) boundary on the topology of a complex (or symplectic) manifold; classification of Legendrian knots; definition and study of capacity-like symplectic invariants for contact manifolds; Smale-type theory for plurisubharmonic functions; metrical properties of the symplectomorphism group; developing the technique of filling by holomorphic discs and its applications. It is important that these problems are at the frontier of several complex variables and symplectic geometry, so both fields will benefit from progress in this direction. Profound connections to mathematical physics also lie in these areas of analysis and geometry.
