Title: Introduction to Tropical Geometry

Abstract: Tropical Geometry is one of the topics for Week 3, and the subject of great amount of recent activity over the last decade. Loosely speaking, it can be described as a piecewise linear version of algebraic geometry, or as non-Archimedean combinatorics. It is based on tropical algebra, where the sum of two numbers is their maximum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of geometric information about their classical counterparts.
In this talk, I will give a gentle introduction to the subject, focusing on some concrete examples and applications to algebraic geometry.