NCMW - Holomorphic and Topological Methods in Symplectic Geometry (2024)

Venue: Indian Statistical Institute, Kolkata

Dates: 3 Jun 2024 to 8 Jun 2024

Symplectic geometry is a branch of mathematics that explores the intrinsic geometric and algebraic properties of symplectic manifolds. Unlike Riemannian geometry,which focuses on the curvature and distances on smooth manifolds, symplectic geometry centers around preserving the symplectic structure, which is a non-degenerate closed 2-form. This structure plays a crucial role in describing classical mechanics, Hamiltonian systems, and other physical phenomena. Symplectic geometry has profound connections to algebraic topology, complex geometry, and mathematical physics, making it a versatile field with applications ranging from fundamental theoretical insights to practical engineering and scientific advancements.
The lectures in the workshop will be on techniques like the J-holomorphic curves, and other topological methods to analyze symplectic and contact structures. The required background is a course in Riemannian geometry, and the initial topics will be accessible to second year PhD students in topology. The latter part of the workshop will feature more recent developments in the subject.

Target Audience:
The School is meant for PhD students working in Geometry and Topology. The topics may also interest students working in complex geometry especially those who are interested in holomorphic techniques in these subjects. The participants must be familiar with elementary Riemannian geometry (curvature and differential forms).