BIRS Workshop Lecture Videos
Analytic and tropical varieties over higher rank valued fields Foster, Tyler
Recent work of Nisse-Sottile, Hrushovski-Loeser, Ducros, and Giansiracusa-Giansiracusa demonstrates that valuation rings of rank >1 play an important role in the geometry of analytic and tropical varieties over non-Archimedean valued fields of rank 1. In this talk, I will present recent work with Dhruv Ranganathan and Max Hully on the geometry of analytic and tropical varieties over higher rank valued fields. I will explain how ideas coming from tame topology can be used to study the geometry of these spaces. I will explain the role that multi-stage degenerations play in this geometry, and if time permits, I will sketch an application of these ideas to the study of tropical and algebraic intersection multiplicities.
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