Universality for tropical maps.

Abstract: I will discuss recent work concerning maps from tropical curves to orthants. A “combinatorial type” of such map is the data of an abstract graph together with slope vectors along the edges. To each such combinatorial type there is an associated moduli space, which parametrises metric enhancements of the graph compatible with the given slopes. This moduli space is a rational polyhedral cone, giving rise to an affine toric variety.

Our main result shows that every rational polyhedral cone appears as the moduli space associated to some combinatorial type of tropical map. This establishes universality (also known as Murphy’s law) for tropical maps. The proof is constructive and extremely concrete, as I will demonstrate. Combined with insights from logarithmic geometry, our result implies that every toric singularity appears as a virtual singularity on a moduli space of stable logarithmic maps.

This is joint work with Gabriel Corrigan and Dan Simms.

algebraic geometrycombinatorics

Audience: researchers in the topic

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Tropical Geometry in Frankfurt/Zoom TGiF/Z

Series comments: Description: An afternoon seminar series on tropical geometry, known as the TGiZ ("Tropical Geometry in Zoom") or the TGiF ("Tropical Geometry in Frankfurt") seminar.

Please send an email to one of the organizers at the latest one day before a session if you wish to receive the Zoom link and password.

Videos of some past talks are available on YouTube here, while some slides can be found here.

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