A Personal Tour Through Symplectic Topology and Geometry

(i) Gromov’s Compactness Theorem for pseudo-holomorphic curves in symplectic manifolds ([23]) and the topology of symplectomorphism groups of rational ruled surfaces (sections 2 and 3, references [1, 2]). (ii) Atiyah-Guillemin-Sternberg’s Convexity Theorem for the moment map of Hamiltonian torus actions ([9, 25]) and Kähler geometry of toric orbifolds in symplectic coordinates (sections 4 and 5, references [3, 4, 5]). (iii) Donaldson’s moment map framework for the action of the symplectomorphism group on the space of compatible almost complex structures ([17]) and the topology of the space of compatible integrable complex structures of a rational ruled surface (sections 6 and 7, references [6, 7]).