Tropical multiplicities from polyvector fields and QFT

Abstract: When considering planar tropical curves satisfying point conditions, Mikhalkin expressed the tropical curves' multiplicities as the product of the multiplicities of their vertices. Such a decomposition of the multiplicity into local computations is very useful in practice, e.g., in the Gross-Siebert program. I will describe joint work with H. Ruddat in which we give such localized tropical multiplicity formulas very generally (in genus 0) using mirror polyvector fields. Our approach involves developing a notion of tropical quantum field theory which works for all genera.

algebraic geometrydifferential geometryquantum algebrasymplectic geometry

Audience: researchers in the topic

Boston University Geometry/Physics Seminar

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