Tropical differential equations and their solutions.

Appears in collection : Tropical Geometry, Berkovich Spaces, Arithmetic D-Modules and p-adic Local Systems

Tropical differential equations were introduced in 2015 by Dima Grigoriev, whose interest was in the computational complexity of finding the supports of power series solutions of systems of linear ODEs. The next year, Fuensanta Aroca, Cristhian Garay and Zeinab Toghani proved a Fundamental Theorem showing that every tropical solution of a differential ideal lifts to a solution over a field. I'll present this theory and some of the developments Zeinab, I and others have achieved since, such as extensions to PDEs and connections to Groebner theory.