Georgia Institute of Technology College of Sciences

Tropical varieties are polyhedral objects that behave like algebraic varieties. They arise in a few different ways -- from polynomials with (max,+) operations, from study of Groebner bases, and from non-archimedean valuations of algebraic varieties. In this expository talk, I will introduce the tropical varieties of ideals in a polynomial ring from the point of view of (max,+) algebra and show how they are related to Groebner theory, Newton polytopes and their subdivisions. I will also discuss their properties and give some examples.