Summer REU 2024

Meeting notes

Notes on tropical geometry

A brief history of tropical algebraic geometry
Tropical numbers
Tropical varieties
Linear tropical varieties
Quadratic tropical varieties
Investigation into tropical tangency loci

Task list

The task list below will grow and change over the course of our project.

Background Material

Classical algebraic geometry

• Affine varieties
• The Algebra-Geometry Correspondence
• The projective plane
• Dual projective space
• Point-line duality
• Duality for projective plane conics

Tropical algebraic geometry

• A brief history of tropical geometry
• Tropical curves
• The tropical projective plane
• Tropical projective plane conics
• Tropical tangency
• Tropical algebra

Investigation

• Duality via tropical tangency
• A hybrid approach: bend loci and congruence varieties
• Summarize previous investigations
• Tropicalize the arguments used in the classical case

Project timeline

Because of various technical issues, I cannot share the live version of the project timeline. As a workaround, I am embedding a snapshot of that timeline below. I'll make sure to update this snapshot whenever I update the timeline.