Georgia Institute of Technology College of Sciences

A matroid is a combinatorial abstraction of an independence structure, such as linear independence among vectors and cycle-free-ness among edges of a graph. An algebraic variety is a solution set of a system of polynomial equations, and it has a polyhedral shadow called a tropical variety. An irreducible algebraic variety gives rise to a matroid via algebraic independence in its coordinate ring. In this talk I will show that the tropical variety is compatible with the algebraic matroid structure. I will also discuss some open problems on algebraic matroids and how they behave under operations on tropical varieties.