Reading Group in Lie Theory + Geometry

Topic

What would you like to learn?

• Lie Theory?
• Theory of Smooth Manifolds, in particular, Riemannian Geometry?
• Applications to Geometric Learning?

Approach

How would you like to learn it?

Books (math/theory and/or engineering/applications)

Discussing and/or implementing important papers

Mini lectures (I can help with these)

Group problem solving/whiteboarding, exploring specific spaces (projective, hyperbolic,.)

Resources by Topic

1. Lie Groups and Lie Algebras

Group-Theoretical Methods in Image Understanding

Kanatani

Lie Groups, Lie Algebras, and Representations

Brian C. Hall

------Optional Prerequisites / Accompanying Material--------

Here’s a somewhat verbose outline/sketch covering useful mathematical preliminaries. Don’t worry if this seems like too much. We can dilate or contract any part according to the group’s background and interests.

2. Intro to Abstract Algebra (Quick 1000ft overview)