Introduction to tropical geometry

Lecturer: Sam Payne - Notes

This course will provide an introduction to tropical geometry for subvarieties of toric varieties over nonarchimedean fields. The first lecture will define the tropicalization of a toric variety and its subvarieties and explain the basic properties of the tropicalization functor. Subsequent lectures will explore the relationship between tropical geometry and nonarchimedean analytic spaces, through limits of tropicalizations, with special attention to curves. As time permits, we will discuss topics of current research interest, such as faithfulness of tropicalizations and lifting theorems for tropical intersections. The following is a preliminary outline of the sequence of lecture topics. 


Lecture 1: Tropicalization of subvarieties of toric varieties
Lecture 2: Limits of tropicalizations
Lecture 3: Tropical geometry of curves
Lecture 4: Integral models, skeletons, and faithfulness
Lecture 5: Tropicalization of intersections

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