Ideas around Symplectic Field Theory
Ideas around Symplectic Field Theory

Helmut Hofer, IAS
Fine Hall 314
Symplectic Field Theory (SFT) is the study of (pseudo)holomorphic curves in symplectic cobordisms and contains GromovWitten theory and symplectic Floer theory as special cases. The algebraic invariants of SFT are obtained by a simultaneous study of infinitely many interdependent first order elliptic systems which exhibit compactness and transversality issues. A treatment of SFT with classical (nonlinear) Fredholm theory, though possible, would be extremely cumbersome. This lead to the development of a new generalized Fredholm theory in a new class of general spaces called polyfolds. In the talk a certain number of ideas are described which might be also useful in different contexts.