V5D6 - Introduction to symplectic geometry

Practical information:

• Course time: Thursday 10--12
• Location: Wegelerstr. 10 - Zeichensaal

Contacts:

• Co-instructor: Nate Bottman
• Email: bottman at mpim-bonn dot mpg dot de

• Co-instructor: Laurent Côté
• Email: lcote@math.uni-bonn.de

Overview of the course:

The subject of symplectic geometry deals with objects called symplectic manifolds. A symplectic manifold is a smooth manifold endowed with a 2-form which is closed and of maximal rank. While it may not be apparent from the definition why these objects should occupy an entire field of mathematics, symplectic manifolds turn out to be extremely rich. Their study is also connected to many other areas of mathematics including algebraic geometry, representation theory, dynamics, etc.

This course aims to provide a first introduction to symplectic geometry, assuming relatively minimal background. We will cover a selection of topics, including: basics of symplectic geometry; constructions of symplectic manifolds; Lagrangians submanifolds; Hamiltonian dynamics.

Importantly, and in contrast to last year's (V5D3), we will not discuss J-holomorphic curves or Floer theory. Students wishing to learn more about Floer theory can consider participating in the seminar (S2D1/S4D1).

The course will be co-taught by Nate Bottman and Laurent Côté in English.

Pre-requisites:

• Analysis on manifolds (V3D3/F4D1)
• Topology 1 (V3D1/F4D1)