Felipe Rincon: Tropical Ideals

Abstract: The past few years have seen a significant effort to give tropical geometry a solid algebraic foundation. In this talk I will introduce tropical ideals, which are homogeneous ideals over the tropical semiring in which each graded piece is “matroidal”. I will discuss joint work with Diane Maclagan studying some of the main properties of tropical ideals, and in particular showing that their underlying varieties are always finite polyhedral complexes. This supports the proposal that subschemes of tropical projective space should be defined by tropical ideals.