Tropical Geometry - Lecture 6 - Structure Theorem | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany)
We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

Lecture VI - Structure Theorem | August 26, 2020

Chapters:
00:00 Definition 3.3.1
15:38 Proposition 3.3.2
16:59 Definition 3.3.4
22:42 Theorem 3.3.5 | Structure Theorem for Tropical Varieties
28:57 Proof Structure
32:50 Realizability Problem
47:53 Questions

Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum 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 information about their classical counterparts.