CIS 610, Spring 2023
Advanced Geometric Methods in Computer Science

Course Information
January 9, 2023

This version (Spring 2023) will cover topics chosen from the following list:

Manifolds, Riemannian Metrics,
Lie Groups, Lie Algebras,
Homogeneous manifolds
Reductive Homogeneous manifolds and
Symmetric Spaces
Commutative Harmonic Analysis on LCA groups
Representations of algebras (L^1(G)),
Unitary Representations of Locally Compact Groups,
Compact Groups, the Peter-Weyl Theorem,
Induced Representations,
An introduction to the "Mackey Machine",
Gelfand Pairs,
With Applications to group equivariant deep learning,
computer vision, and robotics

** Welcome to CIS610! **


Claire Fagin Hall 216, Tu-Th, noon-1:30


Jean H. Gallier, GRW 476, 8-4405,

Office Hours:

Jean : TBA


There will be no official textbook(s). We will use material from several sources and some class notes, including

Latex Help:


[   Grade (Homeworks, Exams)   |  Additional Resources   |  Syllabus   |  Slides and Notes   ]

A Word of Advice :

Expect to be held to high standards, and conversely! In addition to transparencies, we will distribute lecture notes. Please, read the course notes regularly, and start working early on the problems sets. They will be hard! Take pride in your work. Be clear, rigorous, neat, and concise. Preferably, use a good text processor, such as LATEX, to write up your solutions.

It is forbidden to use solutions of problems posted on the internet. If you use resources other than the textbook (or the recommended textbooks) or the class notes, you must cite these references.

Plagiarism Policy

I assume that you are all responsible adults.
Copying old solutions verbatim or blatantly isomorphic solutions are easily detectable.
DO NOT copy solutions from old solution sheets, from books, from solutions posted on the internet, or from friend!
Either credit will be split among the perpetrators, or worse!

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Jean Gallier