L3 Graduate Student Workshop in Symplectic/Contact Geometry

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

This award supports a week long workshop, titled "L3 Graduate Student Workshop in Symplectic/Contact Geometry," held at New Orleans, Louisiana, on January 19-23, 2016. Symplectic Geometry is a field that connects several research areas such as mathematical physics, geometric topology, algebraic geometry, mirror symmetry and string theory. The goal of this workshop is to introduce participants to contemporary research and discuss future directions. Graduate students will give the majority of the talks. The workshop may serve as a pilot for a future annual event for students of symplectic topology and geometry. The focus of the workshop is exploring connections between Weinstein manifolds and contact geometry, with Lefschetz fibrations and algebraic geometry. Weinstein manifolds are central objects of study in symplectic geometry and mirror symmetry. They are often given the structure of Lefschetz fibrations, which describes their geometry in terms of Lagrangian submanifolds of a Weinstein manifold of one dimension less. Alternatively, one can describe the geometry in terms of Legendrian submanifolds in a contact manifold. As contact geometry is generally more flexible, this allows us to make a number of additional geometric cancellations and makes the combinatorics of the computations easier. The workshop will begin with a discussion of the essential objects and tools in the theory, and end with current research and new directions. The workshop webpage is at http://math.stanford.edu/~ksiegel/workshop/main.html.