2nd degree (Master)
Coordinator Office Hours:
Prof Jake Solomon
Lagrangian submanifolds are among the most important structures in symplectic geometry. A basic question is whether there is a canonical representative of an isomorphism class of Lagrangian submanifolds. Special Lagrangian are the natural candidates for this role. In this course, we will learn some basic and some deeper properties of these submanifolds.
Learning outcomes - On successful completion of this module, students should be able to:
Ability to use tools of symplectic geometry and the analysis of partial differential equations to study special Lagrangian submanifolds.
None. However, the lectures will not necessarily be based on any written source. The students are required to know the material of the lectures thoroughly and to be able to use it to solve problems.
Teaching arrangement and method of instruction:
Lecture and exercises.
Background on calibrated submanifolds with an emphasis on special Lagrangians.
Background on Floer cohomology and the Fukaya category.
Applications of Floer theory to the classification of special solutions to Lagrangian mean curvature flow.
Proof of uniqueness of a special Lagrangian in an isomorphism class of the Fukaya category.
Topics in the analysis of the special Lagrangian equation.
Additional Reading Material:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 100 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %