Math 502: Combinatorics II
This is the second semester of an introductory graduate-level course on combinatorics. We will be covering symmetric function theory, Young tableaux, counting with group actions, designs, matroids, finite geometries, and not-so-finite geometries.
Syllabus
For more details, see the Course Syllabus.
Resources
Recommended (but optional) books are listed in the Syllabus above.
Lecture notes will be updated here as the course progresses.
Jan 20, 23 - Intro and Antisymmetrics
Jan 30, Feb 1, 3 - RSK and the Pieri rules
Feb 6, 8, 20 - RSK, Knuth equivalence, and JDT
Feb 13, 15, 17 - Littlewood-Richardson tableaux and crystals
Feb 20, 22, 24, 27 - Crash course on representation theory
March 1, 3 - Characters and the Murnaghan-Nakayama rule
March 6, 8, 10 - Counting with group actions
Apr 10, 12, 14 - Finite Geometries
Apr 17, 19, 21 - Not So Finite Geometries
Office hours
My office is Weber 125, near the west door of the tea room. Come find me:
- Wednesday 10 am and 12 noon, before and after class
- By appointment (Email me at Maria [dot] Gillespie [at] colostate [dot] edu)
- Feel free to knock on my office door for quick questions!
Homework
Homework assignments will be posted here as the course progresses.
Final Projects
Here are the final projects written by the students:
C. Mrozek and A. Romero, Hook Length Formula - History and Proofs by Example
P. Wilson, Promotion and Evacuation
C. Jones, What’s Your Strategy?
K. Brown, Local Evacuation Shuffling and the Pieri Case
I. Rojas, Moduli Spaces of Stable Curves with Marked Points: Examples and Connections to Trees
J. McCann, Solving Linear Intersection Problems with Schubert Varieties