Learning objectives
The goal of the lectures is to introduce the basic definitions, the methods and some results of Symplectic Geometry.
Prerequisites
None
Course unit content
1. Basic notions.
2. Generating functions.
3. Holomorphic curves.
Full programme
1. Basic notions.
Classical mechanics, Hamiltonian diffeomorphisms, Hofer metric; Symplectic manifolds, Lagrangian submanifolds, Arnold conjecture. Examples, symplectic reduction.
2. Generating functions.
Definitions, existence, Poincare's Last Geometric Theorem, Arnold conjecture.
3. Holomorphic curves.
Basic theory, nonsqueezing, Hofer geometry, Floer homology.
Bibliography
McDuff and Salamon, Introduction to symplectic topology, Oxford, 1998.
McDuff and Salamon, J-holomorphic curves and symplectic topology, AMS 2012.
Polterovich, The geometry of the group of symplectic diffeomorphisms, Birkhauser, 2001.
Teaching methods
Lectures. Homeworks will be assigned.
Assessment methods and criteria
Oral examination
Other information
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2030 agenda goals for sustainable development
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