Rigid geometric structures and their automorphism groups - Part 1

By Karin Melnick

Appears in collection : 2024 - T2 - Group actions and rigidity: around the Zimmer program

This mini-course will be an introduction to rigid differential-geometric structures and their automorphisms. It will cover some of the basic theory of G-structures of finite type in the sense of Cartan and a variety of examples. A few major theorems on automorphisms of such structures, such as Zimmer’s Embedding Theorem and Gromov’s Open-Dense Theorem, will be presented, along with some significant applications. In the last section of the course, the plan is to present a 21st-century rigidity result for conformal actions of nilpotent groups on compact pseudo-Riemannian manifolds.

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