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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

DIFFERENTIAL GEOMETRY
cod. 00474

Academic year 2017/18
1° year of course - Second semester
Professor
Leonardo BILIOTTI
Academic discipline
Geometria (MAT/03)
Field
Attività formative affini o integrative
Type of training activity
Related/supplementary
48 hours
of face-to-face activities
6 credits
hub:
course unit
in ITALIAN
lectures timetable unavailable
exam calls
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Learning objectives

The goal of the course is to give to the students, by means of frontal class, the geometrical aspects of isometric actions, and an introduction to symplectic geomety and momentum map

Prerequisites

DIFFERENTIAL GEOMETRY

Course unit content

LIE GROUPS, LIE GROUPS ACTING ON MANIFOLDS AND MOMENTUM MAP

Full programme

An introduction to Lie group and Riemannian Geometry. Bi-invariant metric on Lie group. Proper action. Fiber bundle, Slice Theorem, stratifcation of the orbit space. Compact Lie group, maximal torus and Weyl group. Symplectic manifold, Darboux Theorem, momentum map and Convexity theorems.

Bibliography

ALEXANDRINO, BETTIOL ''LIE GROUPS AND GEOMETRICAL ASPECTS OF ISOMETRIC ACTIONS, ANA CANNAS DA SILVA ''LECTURES ON SYMPLECTIC GEOEMETRY''

Teaching methods

The course counts 9CFUs which corresponds to 48 hours of lectures. The didactic activities is given by frontal class.

Assessment methods and criteria

Verification of the knowledges is achieved by an oral exam.

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