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Curve counting and tropical geometry

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If you have a question about this talk, please contact Macarena Arenas.

The goal of this talk is to appreciate a striking result originally due to Mikhalkin. The question is easy to state: how many degree d curves pass through 3d-1 points in the complex plane. Mikhalkin’s answer illustrates a much—celebrated link between the geometry of polynomials (algebraic geometry) and the geometry of cone complexes (tropical geometry). Cone complexes, unlike algebraic curves, can be drawn on the blackboard: tropical geometry thus gives a powerful tool for visualising problems. Time permitting, I will sketch a modern proof of Mikhalkin’s result.

This talk is part of the Junior Geometry Seminar series.

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