Introduction to Symplectic Topology

Introduction

This is a semester-long Master course at the University of Bonn. This course aims at providing students with a sense of symplectic topology: how it comes from and gradually becomes an interesting and connects to various areas of mathematics. We will roughly follow the historical timeline, starting with the "main branch" of symplectic topology: from Arnold's classical mechanics perspective to Floer's revolutionary theory that is regarded as a common ground of symplectic topology. Then we will select and discuss some other selected branches of symplectic topology, particularly the study of flexibility, Viterbo's isomorphism and the resolution of nearby Lagrangian conjecture.

Prerequisites.

The students are required to have a basic understanding of differential geometry, particularly about smooth manifolds, differential forms, and Lie groups. Some knowledge of algebraic topology are also expected, including familiarity with homology and cohomology theories. Some basic knowledge of complex geometry will be helpful, but not required. Knowledges about partial differential equations, particularly on elliptic PDEs will also be very helpful.

Assessment.

The course will have no problem sets or assignments. The assessment will be based on an oral exam at the end of the course. The oral exam problems consist of compulsary and selective parts. Part 1 is compulsary and students are required to choose one part from 2,3,4 for the oral exam. The compulsary part will consist 50% of the questions, and the selective part will consist the remaining 50%.

Schedule of the Course