This is a graduate topics course on matroids. We will cover the fundamentals of matroid theory, including cryptomorphic definitions, duality, representability, the Tutte polynomial and matroid invariants, and excluded minor theorems. We will also explore connections to graph theory, hyperplane arrangements, and algebraic and tropical geometry. Time permitting, we will discuss recent developments in the field, possibly touching on Baker's matroids over hyperfields and/or the proof of the Heron-Rota-Welsh conjecture by Adiprasito, Huh, and Katz.
Max Kutler, max.kutler(at)yale(dot)edu, LOM 222-B.
Office hours: Drop-in or by appointment.
The early part of the course will draw heavily from Oxley's book, but we will not directly follow any one text for the duration of the course. However, the following references may be useful. (List to be updated throughout the term.)
There will be five homework assignments, each worth up to two points. A score of 5 earns a B+ (P), 7 earns an A- (HP), and 8 earns an A (H).
Homework 1: Due Monday, Feb. 5.
Homework 2: Due Monday, Feb. 26.
Homework 3: Due Wednesday, March 28.
Homework 4: Due Wednesday, April 18.
Homework 5: Due Wednesday, May 2.