Moduli spaces in symplectic topology

Symplectic manifolds arose as a mathematical generalisation of phase space in Hamiltonian mechanics. As they have no local invariants, the construction of invariants is a non-trivial task. Moduli spaces of pseudo-holomorphic curves have proven to be a powerful tool and are by now ubiquitous in the field. I will describe their potential and challenges and how my research provides frameworks to deal with them.