A general theory of tropical differential equations

Abstract: A few years ago Grigoriev introduced a theory of tropical differential equations and how to tropicalize algebraic ODEs over a trivially valued field. In his setup, one looks at formal power series solutions, and tropicalizing is taking the support. I will describe work with Stefano Mereta towards building a theory of significantly more general scope with potential applications to p-adic differential equations. I will describe analogues of valuations, Berkovich analytification, and tropicalization, for algebraic differential equations over a differential field with a non-trivial valuation. The theory is built in the language of idempotent semirings.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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