Past lectures

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Abstract

I propose to give an advanced graduate course about the theory of lattices in locally compact groups including both the classical theory that has been developed mainly during the 60’s and the 70’s of the previous century as well as recent and present progress.

Table of content:

(1) Basic properties and examples (geometric and arithmetic).

(2) Malcev theory for lattices in Nilpotent groups.

(3) Lattices in Solvable groups: Mostow’s theory and recent progress.

(4) The classical theory of lattices in semisimple groups.

(5) Rigidity and Arithmeticity.

(6) Bader–Furman theory: Generalized Weyl groups and new approach for rigidity. (7) The topology of locally symmetric manifolds.

(8) Invariant random subgroups and local convergence of locally symmetric spaces.