7 papers
Residues of a tropical zeta function for convex domains
Nikita Kalinin, Ernesto Lupercio, Mikhail Shkolnikov
We define an -invariant tropical zeta function of a convex domain. In dimension 2 it admits boundary Dirichlet-series representation with summands…
Fibers of phase tropicalizations
Andrei Bengus-Lasnier, Mikhail Shkolnikov
The subject of the present paper is phase tropicalization, which was used crucially in the context of Mikhalkin's correspondence theorem for curve counting in the complex coefficie…
Introduction to non-Abelian Patchworking
Turgay Akyar, Mikhail Shkolnikov
The note introduces a novel concept of non-Abelian patchworking arising as real locus of non-Abelian complex-phase tropical hypersurfaces, the theory of which is now developed enou…
Planar tropical caustics: trivalency and convexity
Mikhail Shkolnikov
Tropical caustic of a convex domain on the plane is a canonically associated tropical analytic curve inside the domain. In this note we give a graphical proof for the classificatio…
tropicalization and lines on surfaces
Mikhail Shkolnikov, Peter Petrov
The paper is based on a talk given by the first author at the Gökova Geometry \& Topology conference in May 2024. The subject is an interplay between the ideas of tropical geometr…
Tropical limit of hyperbolic amoebas of complex analytic surfaces
Peter Petrov, Mikhail Shkolnikov
In this letter, we establish a general fact about the convergence of images of families of closed analytic surfaces in the special linear group un…