Josephine Yu (Georgia Institute of Technology)
Tropical geometry is the geometry over the tropical semiring, which is the set of real numbers where the tropical addition is taking the minimum, and the tropical multiplication is the ordinary addition. As the ordinary linear and polynomial algebra give rise to convex geometry and algebraic geometry, tropical linear and polynomial algebra give rise to tropical convex and tropical algebraic geometry. Tropical algebraic varieties are polyhedral complexes that behave very much like usual algebraic varieties. For example, two tropical quadratic curves in the plane intersect at four points. Tropical geometry has connections to various branches of pure and applied mathematics such as enumerative geometry, computational algebra, dynamical systems, and statistical physics. In this talk, I will introduce tropical varieties and basic results about them.