Math 202B - Applied Algebra II (Winter 2022)
We will cover representation theory of finite groups and symmetric functions with an emphasis on representation theory of symmetric groups and time permitting, polynomial functors.
- Lecture times and location: pre-recorded, posted below
- Instructor: Steven Sam email
- Instructor office hours: Zoom, Thursdays 11:30AM-12:20PM or by appointment
- TA office hours: Zoom, Fridays 1-3PM
- Discord server: link (we'll use this to discuss the class)
There is no single textbook for this course, but you may find some of the following books useful:
- Fulton, Harris, Representation Theory
- James, The Representation Theory of the Symmetric Groups
- Sagan, The Symmetric Group
- Serre, Linear Representations of Finite Groups
- Stanley, Enumerative Combinatorics Vol. 2
Turn in all assignments through Gradescope.
My notes for the course
- Notes (last updated 3/3/22)
We will go by weeks rather than individual lectures. I will break up videos based on logical stopping places rather than set time limits.
Each week corresponds to roughly 5-7 pages of the course notes (how much I cover in an in-person lecture).
Unfortunately there may be small mistakes in the videos. I list them in the video description if that happens.
I list some sections from the reference books above that are related to the lecture.
- Week 1 (Jan 3)
- Week 2 (Jan 10)
- Notes: Sections 1.5-1.8
- Serre: 2.3-2.5, 3.1-3.3, 5.1, 5.3, 5.8, 6.1, 7.1-7.2
- Videos: Lecture 4, Lecture 5, Lecture 6
- Notes from lectures: Lecture 4, Lecture 5, Lecture 6
- Week 3 (Jan 17)
- Week 4 (Jan 24)
- Week 5 (Jan 31)
- Week 6 (Feb 7)
- Week 7 (Feb 14)
- Week 8 (Feb 21)
- Week 9 (Feb 28)
- Week 10 (Mar 7)