Introduction to Cohomology of Arithmetic Groups

Manish Patnaik (University of Alberta)

Sep 3, 2024 — Dec 9, 2024

About the course

The most basic example of an arithmetic group is $Γ = S L_{n} (Z),$ and understanding the cohomology of this group (and its close relatives) will be the basic theme of this course. The cohomology we are interested in can also be identified with that of the locally symmetric space $Γ ∖ X$ where, in this case, $X = S L_{n} (R) / S O (n)$ is a generalization of the (complex) upper half plane. As such, a diverse set of techniques, stemming from geometry, topology, harmonic analysis, and number theory can be used to analyze the situation. After carefully developing the basics of the subject, we will present some of the major developments in this area (mostly from the 1960s-1970s), and then end with an overview of modern directions.

Registration

This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

Enrollment Details

Course Name: Topics in Algebra
Date: Sep 3, 2024 — Dec 9, 2024
Course Number: - All Students: MATH 681
Section Number: - Students at UAlberta: LECTURE B1 - Students **not** at UAlberta: Lecture 800
Section Code: - Students at UAlberta: 54832 - Students **not** at UAlberta: 54986

Instructor(s)

Manish Patnaik
patnaik@ualberta.ca
University of Alberta

For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website

Other Course Details

Lecture Times

Dates: Sep. 3 - Dec. 9
Class Time: Tuesday/Thursday, 16-17:20 (Mountain Time)

Remote Access

The lecturer will use a tablet connected to zoom/camera to live stream lectures and notes. Hand written (from table) and typed lecture notes will be distributed.