Mathematics | University of Parma

Professor
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

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

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DIFFERENTIAL GEOMETRY cod. 00474