Jeffrey Herschel Giansiracusa

Tropical geometry has become a powerful toolset for tackling problems in algebraic geometry, combinatorics, and number theory.  The basic objects have traditionally been considered as certain polyhedral sets and heuristically thought of as algebraic objects defined over the real numbers with the max-plus semiring structure.  I will explain how to realize this within an extension of scheme theory and describe the particular form of the equations of tropical varieties in terms of matroids.