Generalising Kapranov’s Theorem for hyperfields and RAC maps

Abstract: Kapranov’s theorem is a foundational result in tropical geometry. In this talk we will discuss developments towards understanding a generalised hyperfield version of Kapranov’s Theorem. We will establish the relevant building blocks from the algebraic setting of hyperfields, which allow addition to be multival- ued operation. We will then introduce Relatively Algebraically Closed (RAC) hyperfield homomorphisms. This property is the key tool leveraged to formulate a generalised version of Kapranov’s theorem. I will present examples of RAC maps and describe the progress towards the classification of this property.

This will contain joint work with Ben Smith (Manchester).

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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The password for the zoom room is 123456