Georgia Institute of Technology College of Sciences

We say that a set is convex if for any two points in the set, the straight line segment connecting them is also contained in the set.  For example, a triangle, a square, a cube, a ball are all convex sets. We typically speak of convex sets in Euclidean space with the ordinary addition and multiplication operations. What happens if we replace addition with taking the minimum between two elements, and multiplication with ordinary addition? These are the tropical arithmetic operations and using these we can define tropical convexity. What does it mean for a set to be tropically convex? What does a tropical triangle look like? In this talk we will answer these questions and explore how ordinary and tropical convexity interact.