Lie Groups - M1 - 8EC

Prerequisites
Basic knowledge of linear algebra, analysis, topology, group theory and differential geometry. It is recommended that the student has already followed (at least) one course on each of these subjects. From topology: open/closed sets, continuity, compactness, connnectedness, metric spaces, Hausdorff, local compactness. The following notions from differential geometry will appear in the course: smooth manifolds, submanifolds, smooth maps, tangent spaces, vector fields, flow/integral curves of vector fields, differential forms, integration with differential forms, immersions and submersions. The more advanced of these can be learned during the course or treated as a black box, but (from experience in 2020) familiarity with the basic parts is indispensible.

Aim of the course
The aim of this course is to give a thorough introduction to the theory of Lie groups.
Topics that will be covered include:

  • general properties of Lie groups (subgroups, homomorphisms, quotients),
  • the exponential map and the Lie algebra of a Lie group,
  • smooth group actions and invariant integration,
  • harmonic analysis on compact Lie groups, up to the Peter-Weyl theorem.

Lecturers
Dr. Maarten Solleveld (Radboud Universiteit Nijmegen)