Given a scheme X over Z and a hyperfield H which is equipped with a topology which
satisfies certain conditions, we endow the set X (H) of H-rational points with a natural …

We introduce tropical spectrahedra, defined as the images by the nonarchimedean
valuation of spectrahedra over the field of real Puiseux series. We provide an explicit …

The main aim of this article is to study and develop valuation theory for Krasner hyperfields.
In analogy with classical valuation theory for fields, we generalise the formalism of valuation …

We present a massively parallel framework for computing tropicalizations of algebraic
varieties which can make use of symmetries using the workflow management system GPI …

We consider a binary classifier defined as the sign of a tropical rational function, that is, as
the difference of two convex piecewise linear functions. In particular, the set of functions …

We prove a fundamental theorem for tropical partial differential equations analogue of the
fundamental theorem of tropical geometry in this context. We extend results from Aroca et al …

We extend the fundamentals for tropical convexity beyond the tropically positive orthant
expanding the theory developed by Loho and V\'egh (ITCS 2020). We study two notions of …

We study real and positive tropicalizations of the varieties of low rank symmetric matrices
over real or complex Puiseux series. We show that real tropicalization coincides with …

In 1957, M. Krasner described a complete valued field (K, v) as the inverse limit of a system
of certain structures, called hyperfields, associated with (K, v). We put this result in purely …

Maximal Mumford Curves from Planar Graphs arxiv:2404.11838v1 [math.AG] 18 Apr 2024 Page
1 Maximal Mumford Curves from Planar Graphs Mario Kummer, Bernd Sturmfels and Raluca …