Mathematics 797SG - ST-Symp Geom and Floer Theory

Symplectic geometry is a central topic in mathematics with connections to algebraic geometry, differential geometry, complex geometry and topology. A major tool which has generated much recent research interest and has many applications in a diverse set of fields, is Floer theory. This course will denote the beginning portion of the semester on a general introduction to symplectic geometry. Once the necessary background is complete, the course will introduce Floer theory, defined using holomorphic curves. The course will also discuss applications and computations of the theory in low-dimensional topology, and possibly symplectic dynamics. Prerequisites: Smooth manifolds and differential forms (Math 703-704), basic topology (Math 671), Complex Analysis (Math 621). Some exposure to homology and cohomology is very helpful but not absolutely necessary (for example, Algebraic Topology Math 782, 781 or 797AT and/or Homological Methods Math 797EG).