MATH 263Z: Lagrangian Floer theory and Fukaya categories

Course goals:

This graduate topics course will survey various aspects of Lagrangian Floer theory, starting with its introduction to address classical conjectures in symplectic geometry, and the rich algebraic structures captured by the Fukaya category. These will also be discussed through the lens of homological mirror symmetry. Further topics include family Floer cohomology and local-to-global principles for Fukaya categories.

Prerequisites: graduate-level differential geometry and algebraic topology (Math 230a and 231a or equivalent).  Some prior familiarity with symplectic geometry strongly recommended. (Suggested reading: Ana Cannas, Lectures on Symplectic Geometry, through section 18). Prior familiarity with algebraic geometry and homological algebra will be helpful but is not strictly required.

Students who need a grade will be expected to attend lectures and to complete assignments, write a final paper, and for undergraduates, a brief oral examination related to one of the assignments.