Algebraic matroids and tropical varieties

Research Horizons Seminar
Wednesday, November 16, 2016 - 12:00
1 hour (actually 50 minutes)
Skiles 006
Georgia Institute of Technology
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.