Lagrangian Geometry of Matroids

Matroid theory is an abstraction of linear independence that has connections to various aspects of combinatorics, algebra, and geometry. I will outline a recent approach to the study of matroids that brings some tools from complex algebraic geometry into play, using ideas from tropical geometry. In particular, positivity properties of a Lagrangian model for a matroid can be used to settle two 1980's conjectures of Brylawski and Dawson on inequalities satisfied by certain sequences of integers associated with a matroid.

This is joint work with Federico Ardila and June Huh.