Math 581

Welcome to Math 581!

  • Instructor: Andy Wilson
  • Instructor email: andwils AT math DOT upenn DOT edu
  • Lecture: Tuesday and Thursday, 12-1:20 PM, David Rittenhouse Labs 4C4
  • Primary textbook:
    • Enumerative Combinatorics, Vol. 2 - Richard Stanley (specifically Chapter 7)
  • Supplementary textbooks (optional):
    • The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions - Bruce Sagan
    • The q,t-Catalan Numbers and the Space of Diagonal Harmonics - Jim Haglund
  • Office hours: 2-3 PM, Wednesdays, DRL 3C7
  • Homework: There will be a few homework assignments throughout the semester.
  • Presentations: Students will give presentations throughout the semester.
  • Material: The goal of this course is to introduce students to the theory of symmetric functions. Symmetric functions are a major branch of modern combinatorics. They have been used to solve problems in areas such as enumerative combinatorics, group theory, algebraic geometry, and representation theory. They are also fascinating in their own right, as displayed in Macdonald polynomial theory. I will introduce the theory of symmetric functions via a series of lectures based on Chapter 7 of Stanley's Enumerative Combinatorics, Vol. 2. Students will give presentations throughout the semester. The aim of these presentations is to show the ways in which the material we are learning appears in the current literature. With luck, there will be time at the end of the semester to investigate some related topics, such as Macdonald polynomials, quasisymmetric and nonsymmetric polynomials, or Schubert calculus.
  • Background: The main prerequisite is "mathematical sophistication," as Stanley is not an easy text. Some experience in combinatorics (at the level of an undergraduate course) is desirable, but not required. Please email/see me if you are unsure if you are prepared for the course.
  • Grade: Final grades will be based on presentations and homework assignments. There will be no exams.
  • Resources:
    • Here are a few applets/programs which I have found useful - note that none of these are my own creations.
    • Here are the slides I went over in class:
      • Knot invariants
      • The Delta Conjecture