Tropical Geometry - Lecture 3 - Fields and Varieties | 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 III - Fields and Varieties | August 21, 2020 Chapters: 00:00 Introduction 02:44 Lemma 2.1.1 07:05 Theorem 2.1.5 14:32 Value Group 20:53 Ultrametric 24:15 Torus 32:56 Morphism 40:24 Grassmanian 44:21 Lemma 2.2.12 49:12 2.3 | Polyhedral Geometry 52:11 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.

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