course dates credits
Differential Geometry and Group Theory Oct 1 - Nov 7 4
teachers schedule term
Marco Serone 11:30 - 13:00 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
  • 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
  • Representations of SL(2,R)
  • Verma modules and infinite dimensional representations

    • Online Resources:

    Filename Size (bytes) Date Modified
    SISSA_Groups_course_MS_2025.pdf 956.95 KB Nov 11 2025 1:31 PM