Symplectic Geometry and Topology
September 1 - December 11, 2015
Symplectic and Contact Geometry has its roots in the mathematical description of analytical mechanics where the phase space of a mechanical system is the cotangent bundle of its configuration space with symplectic form, equal to the exterior derivative of the action or Liouville 1-form, that is preserved under the time evolution of the system. The modern developments of the subject were initiated by V.I. Arnold around 1980.
In a groundbreaking paper of 1985, M. Gromov introduced pseudo-holomorphic curves in symplectic geometry that were shortly thereafter used in seminal work by A. Floer. This lead to proofs of some of Arnold’s conjectures but more importantly changed the nature and direction of the entire research field.
Since the field of Symplectic and Contact Topology was initiated two and a half decades ago, it has grown enormously and unforeseen and deep connections to other areas of mathematics and physics have been established. Today the area is vast and constitutes a both central and vivid part of mathematics.
The main purposes of the research program are the following:
- To promote the flow of ideas between different areas of symplectic and contact geometry.
- To lead to new breakthroughs and solutions of some of the main problems in the area.
- To discover new applications of symplectic and contact geometry in mathematics and physics.
- To give the junior participants a broad perspective of the subject and a working knowledge of its diverse techniques.
The main themes for the program will be:
- Algebraic structures and holomorphic curves.
- Symplectic rigidity and differential topology.
- Mirror symmetry and low dimensional topology..