Student Combinatorics Seminar

In linear algebra, graph theory, and other areas, one sometimes encounters a collection of vectors and is interested in which subsets are linearly independent. A matroid is a structure intended to reduce this situation to its essentials and characterize linear independence purely in terms of subsets.

In the first part of this talk, we'll introduce a few of the many equivalent definitions of matroids, emphasizing the inspiration from linear algebra. In the second part, we'll turn around and look at the ways matroid theory diverges from linear algebra. The definition of a matroid turns out to be quite loose, allowing many matroids not arising from sets of vectors to slip through. However, we'll see that their presence not only has its own elegant consequences, but is also unavoidable. Speaker(s): Will Dana