**Office Hours:**
I will have office hours just for this class on Wednesdays, 9:30-10:50
AM in my office, East Hall 2844.
I also have office hours scheduled for Math 214 on
Thursday 1:00-2:20 PM (Zoom) and Friday 9:30-10:50 AM (East Hall 2844).
You may come during those times as well, but you may find a crowd.

**Webpage:** `http://www.math.lsa.umich.edu/~speyer/668`

**Level:** Graduate students who are comfortable with abstract
linear algebra (vector spaces, tensor products, symmetric and wedge
product), who have some familiarity with groups and
representation theory, and a high level of mathematical maturity.
There will be a few manifolds and integrals.
Towards the end of the term, I will start using the language of categories.

**Anticipated topics:** We will definitely cover: Classical combinatorics of symmetric
polynomials, Young tableaux, generalities on representation theory of compact and of
reductive groups, construction of the irreducible representations of
GL_{n}. We will likely cover: RSK, jeau de tacquin,
crystals, the Littlewood-Richardson rule.
Additional topics I'd like to fit in as possible: Representation theory of GL_{n}, webs,
standard monomial theory, connections to cluster algebras and total
positivity, connections to quiver representation theory, honeycombs, puzzles.

I previously taught this course in 2012; here is what I covered then.

**Student work expected:** I will give problem sets every week, due
Wednesday evenings on Gradescope.
I will also require students to take turns serving as
scribe for the course, meaning taking TeXed notes on what we have covered
that day.
Finally, I will require you all to either write an expository 10-15
page paper, or to prepare a 30-50 minute talk on some subject in
combinatorial representation theory that interests you.

Here is a list of possible topics and references; and I am glad to discuss other options.
You can satisfy this last requirement by giving a talk on an
appropriate topic in the student combinatorics seminar. If you are
interested in speaking, please contact the organizers, Will Dana
(`willdana@umich.edu`) and Scott Neville
(`nevilles@umich.edu`).
The student combinatorics seminar meets Mondays at 4 PM in East Hall
3866.
I encourage you to attend the student combinatorics seminar, and the
regular combinatorics seminar, in general.

I don't intend for you to need to consult books and papers outside your notes. If you do consult such, you should be looking for better/other understanding of the definitions and concepts, not solutions to the problems.

You

All problem sets should be turned in through Gradescope. You should have gotten a notification that you were enrolled in the Gradescope course; if you didn't, please write me.

- Problem Set 1 (TeX), due Wednesday, September 7, 11:59 PM.
- Problem Set 2 (TeX), due Wednesday, September 14, 11:59 PM.
- Problem Set 3 (TeX), due Wednesday, September 21, 11:59 PM.
- Problem Set 4 (TeX), due Wednesday, September 28, 11:59 PM.
- Problem Set 5 (TeX), due Friday, October 7, 11:59 PM because of Yom Kippur.
- Problem Set 6 (TeX), due Friday, October 14, 11:59 PM.
- Problem Set 7 (TeX), due Monday, October 31, 11:59 PM.
- Problem Set 8 (TeX), due Friday, November 11, 11:59 PM.
- Problem Set 9 (TeX), due Friday, November 18, 11:59 PM. This is the last problem set!

All students will be required to take turns scribing notes for this file. When it is your turn to scribe, download the template file and write in a summary of what happened in class that day. Then e-mail it to me. The deadline for editing the notes is 24 hours after the lecture. I will, in turn, proofread and edit your entries in the next 24 hours and post them back to this webpage, so that the class always has a good record of what we have covered. You are welcome to download and read the source of the notes but please do your writing in the template file; my experience is that it is easier for me to resolve merge conflicts when I copy your text into the master file than if you edit the master file directly.

If you do not know LaTeX, you should learn! I can suggest sources; I also find TeX.stackexchange incredibly useful for specific questions.

If you have forgetten when you are scheduled to write the notes, you can check here.

In the week of October 3-7, we took a break from lectures and solved problems about the basics of finite dimensional representation theory. The problems can be found here. We also had an in class problem solving session on the "unitary trick" on October 21; those problems can be found here.