PhD in Mathematics- Symplectic Geometry and Topology in Stanford United States | Stanford University

Symplectic topology intersects with multiple branches of mathematics, including low-dimensional topology, algebraic geometry, representation theory, Hamiltonian dynamics, integrable systems, mirror symmetry, and string theory. This field exhibits an intriguing blend of both rigid and adaptable characteristics. The symplectic topology research team at Stanford currently investigates holomorphic curve moduli spaces and their transformations during surgical procedures, Symplectic Field Theory with its relative forms, quasi-states and quasi-morphisms theory, along with existence and flexibility findings concerning Stein structures, Weinstein manifolds, and higher-dimensional contact structures.