course dates credits
Differential Geometry and Group Theory Oct 3 - Nov 10 4
teachers schedule term
Marco Serone 10:00 - 11:30 1

Program:

  • Differentiable manifolds: vector fields, differential forms, integration, Lie derivative
  • Lie groups: action of groups on manifolds, Lie algebras
  • Riemannian geometry: metric, connections, curvature, (conformal) Killing vectors, Hodge isomorphism
  • Homology and de Rham cohomology
  • Fibre bundles: vector and principal bundles, connections
  • Lie algebras: simple and semi-simple algebras, Killing form, Cartan-Weyl basis, weights, Cartan matrix and Dynkin diagrams, classification and construction of simple Lie algebras, Weyl group, congruence classes, low-rank examples
  • Highest-weight representations: Dynkin labels, Freudenthal multiplicity formula, Casimir operators, Dynkin index, tensor product decomposition, su(N) and Young diagrams, characters
  • Real forms and compact Lie groups: split and compact real form
  • Subalgebgras
  • Poincare' and conformal groups
  • Spinors in various dimensions
  • Verma modules and infinite dimensional representations

    • Prerequisites:

    Books:

    Online Resources:

    Filename Size (bytes) Date Modified
    SISSA_Groups_course.pdf 874.24 KB Nov 16 2021 10:18 AM