Math 601: Advanced Combinatorics I
This course will focus on the combinatorics of Young tableaux, crystal bases, root systems, Dynkin diagrams, and symmetric functions arising in representation theory of matrix groups and Lie algebras.
Lectures will be at 1 pm on MWF in Engineering building B-4.
Details
Here are the Lecture Notes. These will be added to and updated throughout the course, and some lecture notes will simply be hand written if I don’t have time to type it all.
For more details, see the Course Syllabus. All other information will be posted to Canvas.
Homework
More lecture notes, copied from 2020 but sorted according to topic
Combinatorics of sl2 representations and bracketing rule
Stembridge axioms for type A crystals
Weyl group reflections and crystals
Flag varieties and Springer theory
Chromatic symmetric functions and Hessenberg varieties
Proof of the Stanley-Stembridge Conjecture: Part I preliminaries and overview
Proof of the Stanley-Stembridge Conjecture: Part II: the modular law and proof outline
External: Stanley’s notes on evacuation and promotion
External: Crystals for Dummies by Mark Shimozono
External: Springer Correspondence notes by Sam Gunningham
External: Proof of the Stanley-Stembridge Conjecture by Hikita