This is an introductory course in symplectic geometry. We will cover some foundations of symplectic geometry (such as local theory, Lagrangian submanifolds and Hamiltonian flows). The last part of the course will be devoted to symplectic capacities and some rigidity results.
Learning objective
Get acquainted with the basics of symplectic geometry
Literature
- Lectures on Symplectic Geometry, by A. Cannas da Silva (Springer) - Introduction to Symplectic Topology, by D. McDuff and D. Salamon (Oxford) - Symplectic Invariants and Hamiltonian Dynamics, by H. Hofer and E. Zehnder (Birkhäuser)
Prerequisites / Notice
Prerequisites: Familiarity with differential geometry (in particular, differential forms and vector fields on manifolds) and with topology (including elementary algebraic topology) will be assumed.
Competencies
Subject-specific Competencies
Concepts and Theories
assessed
Method-specific Competencies
Analytical Competencies
assessed
Problem-solving
assessed
Personal Competencies
Creative Thinking
fostered
Critical Thinking
fostered
Performance assessment
Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course