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Degenerations and expansions, and a trip to the tropics

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If you have a question about this talk, please contact Alexis Marchand .

In many cases, breaking things into pieces makes them easier to study, and it turns out this also applies to the area of enumerative geometry (aka the study of counting geometric objects on a variety X). When a variety degenerates (i.e. breaks) into a union of toric varieties, it has been shown that curve counting on the original variety can be recovered from “logarithmic” curve counting on the smaller toric varieties! One can study logarithmic enumerative geometry via a type of surgery on X called expansions, and expansions arise naturally if we take an excursion to tropical geometry.

This talk is part of the Junior Geometry Seminar series.

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