### The Geometry of Monoids: An Introduction to Algebraic and Tropical Toric Varieties for Everyone (or Almost Everyone)

By Martin Ulirsch

February 25, 2013

#### Abstract

First we are going to classify a certain class of monoids using polyhedral geometry. In a second step we are going to use these monoids to give a simultaneous definition of algebraic and tropical toric varieties. These varieties carry a natural action by an algebraic/tropical torus, whose orbits can be described in terms of polyhedral geometry.
This talk does not require knowledge of algebraic geometry. It gives the background for my talk on Cox rings in the Junior Arithmetic and Algebraic Geometry Seminar on Tuesday, February 26, at 4pm in Kassar 205.