Talking About Combinatorial Objects Student Seminar: Menagerie of Matroids

Seminar | October 6 | 12-1 p.m. | 748 Evans Hall

 Theo McKenzie, Mario Sanchez, Chris Eur, UC Berkeley

 Department of Mathematics

**Note unusual time**

This talk is intended to expose the audience to a variety of important concepts or constructions in matroid theory that may reappear in later talks.

Theo will discuss the greedy characterization of matroids. Kruskal's greedy algorithm finds the minimum or maximum weight of a spanning tree of a weighted graph. If I is a collection of subsets of E, we will show how this algorithm successfully finding a maximal member of I with maximum weight for any weight function is equivalent to (E,I) being a matroid.

Mario will introduce the lattice of flats of a matroid and characterize which lattices arise in this way. Then, he'll define the characteristic polynomial of a matroid and show that this polynomial encodes some interesting properties of combinatorial objects.

Time permitting, Chris will do the following in order: 1. give a M2 demonstration of the matroids package that our very own Justin Chen wrote, 2. discuss what a Bergman fan of a matroid is, and 3. discuss an important invariant of a matroid called the Tutte polynomial.