Abstract:
We will provide a theory of polyfolds and abstract perturbations for holomorphic discs. Applications make it possible to prove instances of the Weinstein conjecture and to answer fillability questions for large classes of contact manifolds. Connections to number-theoretic concepts will be drawn via the study of Gromov-Witten invariants. The aim is to investigate whether generating series of Gromov-Witten invariants are Fourier expansions of certain modular forms. This will help us to detect finer structures of Gromov-Witten invariants for non-Kähler manifolds.