Interactions between topology and geometry in low dimensions

This PhD project will delve into the area of low dimensional topology. In the realm of 3-manifolds the topological and the geometric structures inform each other. These interactions are less strong in dimension 4, but gain prominence when studying 3-manifolds as boundaries of 4-manifolds. The student will explore the connections between topology and contact and symplectic geometry using tools such as handle decompositions, Kirby calculus, Dehn surgeries and Lefschetz fibrations.