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Math 601: Advanced Combinatorics I

This course will focus on the combinatorics of Young tableaux, crystal bases, root systems, and symmetric functions arising in representation theory.

Lectures will be held at 3:00 PM MWF. If weather permits we will be outdoors outside of Weber Hall. All lectures (including outdoors) will be recorded. When weather does not permit, we will meet on Zoom.

Zoom Meeting Room ID: 142-012-467

The password is the number of distinct ways to rearrange the numbers in the Zoom meeting ID.


Here are the Lecture Notes. These will be added to and updated throughout the course.

For more details, see the Course Syllabus. All other information will be posted to Canvas.


Homework 1

Homework 2

Homework 3

Cumulative Homework A

Homework 4

Homework 5

Homework 6

Cumulative Homework B

Homework 7

Homework 8

Homework 9

Cumulative Homework C

Homework 10

In-Class Notes

Lecture 7 Notes - Representations of sl2 Part 1

Lecture 8 Notes - Representations of sl2 Part 2

Notes from Sept 14 Lecture

Notes from Sept 16 and 18 Lectures

Notes from Sept 21 Lecture

Notes from Sept 23 Lecture

Notes from Sept 25 Lecture

Lecture Notes, September 28, 30, and October 2 - Combinatorics of tableau crystals for sl3

Lecture Notes, Oct 5 - More sl3 combinatorics

Lecture Notes, Oct 7,9 - representation theory of sln

Lecture Notes, Oct 12-14

Lecture Notes, Oct 16

Lecture Notes, Oct 19

Lecture Notes, Oct 21-23

Lecture Notes, Oct 28

Lecture Notes, Oct 30

Lecture, Nov 2

Lecture Notes, Nov 2

Lecture Notes, Nov 4

Lecture Notes, Nov 6

Lecture Notes, Nov 9

Lecture Notes, Nov 11

Lecture Notes, Nov 13

Lecture Notes, Nov 16

Lecture Notes, Nov 18

Lecture Notes, Nov 20

Lecture, Nov 30

Lecture, Dec 2

Lecture Notes, Nov 30 - Dec 2

Lecture Notes, Dec 4-9