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
Course unit content
LIE GROUPS, LIE GROUPS ACTING ON MANIFOLDS AND MOMENTUM MAP
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.
ALEXANDRINO, BETTIOL ''LIE GROUPS AND GEOMETRICAL ASPECTS OF ISOMETRIC ACTIONS, ANA CANNAS DA SILVA ''LECTURES ON SYMPLECTIC GEOEMETRY''
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.