Combinatorics Seminar - James Maxwell (University of Bristol)


Speaker: James Maxwell (University of Bristol)

Title: 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 multivalued 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).