About
This is the webpage for a minicourse about tropical geometry.
This page is still under construction!
Contact Info
- email: spcox@umich.edu
- office: EH 4828
- site: homepage
Tropical Geometry Textbooks, Notes and Lectures
Here are some resources on tropical geometry. If you know of any others, let me know!
- Sturmfels' Video Lectures youtube
- Introduction to Tropical Geometry by Maclagan and Sturmfels UMich library link, errata
- Essentials of Tropical Combinatorics by Michael Joswig book webpage
- Tropical Geometry by Mikhalkin and Rau pdf
- Triangulations by De Loera, Rambau and Santos UMich Library
- Notes from a mini-course by Brugallé, Itenberg, Mikhalkin, and Shaw arXiv
- Smooth tropical surfaces with infinitely many tropical lines by VigelandUMich link
Computer Algebra Software for Tropical Geometry
Day 1: Tropical Language and Some Applications
Reference: ITG chapter 1.
We will begin by discussing tropical operations, and tropicalization, using polynomials in one an two variables for examples. I will then talk about how notions of smoothness, genus, and multiplicity can be interpreted tropically. We will finish by stating Mikhalkin's theorem and Kontsevich's reccurrence relation.
Day 2: Tropical Hypersurfaces
Day 3: Tropical Linear Spaces
Day 4: Tropical Polytopes