Tropical differential equations

Abstract: In 2015 Dimitri Grigoriev introduced a way to tropicalize differential equation with coefficients in a power series ring and defined what a solution for such a tropicalized equation should be. In 2016 Aroca, Garay and Toghani proved a fundamental theorem analogue to the fundamental theorem of tropical geometry for power series over a trivially valued field. In this talk I will introduce the basic ideas moving then towards a functor of points approach to the subject by means of the recently developed tropical scheme theory, as introduced by Giansiracusa and Giansiracusa, looking at solutions to such equations as morphisms between so-called pairs. I will also give a generalisation to power series ring with non-trivially valued coefficients and state a colimit theorem along the lines of Payne's inverse limit theorem.

algebraic geometrycombinatorics

Audience: researchers in the topic

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.