An Introduction to Geometry and Dynamics on Semisimple Lie Groups - Part 1

Explore the fundamental concepts of semisimple Lie groups, their structure theory, discrete subgroups, and asymptotic behavior in this comprehensive lecture. Delve into the intricacies of semisimple algebras, irreducibility, and structural properties. Examine geometry units, flats, and connected components through various examples. Investigate sign changes and abstract language within the context of these mathematical structures. Gain valuable insights from Jean-François Quint, a researcher from CNRS and the University of Bordeaux, as he presents the first part of a three-part series on geometry and dynamics in semisimple Lie groups.

Introduction
What is a semisimple algebra
The notion of irreducibility
Structural Property
Geometry Units
Flats
Connected Component
Connected Component Examples
Sign Changes
Abstract Language