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 Gromov-Witten 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.