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Università degli Studi di Parma Università degli Studi di Parma
Second cycle degree course in
Mathematics
Università degli Studi di Parma
Department of Mathematical, Physical and Computer Sciences

SYMPLECTIC GEOMETRY
cod. 1007485

Academic year 2017/18
1° year of course - Second semester
Professor
Academic discipline
Geometria (MAT/03)
Field
A scelta dello studente
Type of training activity
Student's choice
48 hours
of face-to-face activities
6 credits
hub:
course unit
in ENGLISH
lectures timetable unavailable
exam calls
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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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