The Fundamental theorem of tropical differential algebra over nontrivially valued fields and the radius of convergence of nonarchimedean differential equations

We will discuss a fundamental theorem for tropical differential equations analogue of the fundamental theorem of tropical geometry in this context. We extend results from Aroca et al. and from Fink and Toghani, working only in the case of trivial valuation as introduced by Grigoriev, to (partial) differential equations with power series coefficients over any valued field. To do so, a crucial ingredient is the framework for tropical differential equations introduced by Giansiracusa and Mereta. As a corollary of the fundamental theorem, the radius of convergence of solutions of a differential equation over a nontrivially valued field can be computed tropically. This talk is based on results appearing in arXiv:2303.12124, joint with F. Gallinaro.