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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
NOT ASSIGNED
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

- - -

2030 agenda goals for sustainable development

- - -

Contacts

Toll-free number

800 904 084

Segreteria studenti

E. segreteria.scienze@unipr.it
T. +39 0521 905116

Quality assurance office

Education manager
dott.ssa Giulia Bonamartini
T. +39 0521 906968
Office E. smfi.didattica@unipr.it
Manager E.giulia.bonamartini@unipr.it

President of the degree course

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Faculty advisor

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Career guidance delegate

Prof. Francesco Morandin
E. francesco.morandin@unipr.it

Tutor Professors

Prof.ssa Alessandra Aimi
E. alessandra.aimi@unipr.it

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Prof. Adriano Tomassini
E. adriano.tomassini@unipr.it

 

Erasmus delegates

Prof. Leonardo Biliotti
E. leonardo.biliotti@unipr.it

Quality assurance manager

Prof.ssa Alessandra Aimi
E. alessandra.aimi@unipr.it

Internships

Prof. Costantino Medori
E. costantino.medori@unipr.it

Tutor students

Dott.ssa Fabiola Ricci
E. fabiola.ricci1@studenti.unipr.it