Lectures related to Linear Lie Groups: Definitions and Theorems

Covers Riemannian connections, emphasizing their properties and significance in geometry.

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Covers the precise description of the relative positioning of objects in space.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Covers Lie Algebra, focusing on vector space and multiplication law.