Special Hamiltonian Circle Actions on Symplectic 4-Manifolds and Lagrangian Surfaces

In this project we introduce a special type of Hamiltonian circle actions on symplectic 4-manifolds. We will investigate their basic properties and establish initial relevant classification results. Furthermore, we will apply these special group actions to study monotone Lagrangian surfaces in symplectic 4-manifolds with almost toric fibrations like weighted projective planes and beyond.