Related papers: Tropicalisation for Topologists
We give an introduction to Tropical Geometry and prove some results in Tropical Intersection Theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
Tropicalizations form a bridge between algebraic and convex geometry. We generalize basic results from tropical geometry which are well-known for special ground fields to arbitrary non-archimedean valued fields. To achieve this, we develop…
These condensed notes treat some basic notions in Tropical Geometry (varieties, cycles, modifications, equivalence). These topics are to be extended, illustrated and included to the upcoming book project…
The main aim of this paper is to show the interconnections between {\L}ukasiewicz logic and algebraic geometry using algebraic, geometric and logical instruments. We continue our investigation into a new algebraic geometry based on…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
This friendly introduction to tropical geometry is meant to be accessible to first year students in mathematics. The topics discussed here are basic tropical algebra, tropical plane curves, some tropical intersections, and Viro's…
We survey some results on toric topology.
This basic introduction to tropical geometry is hopefully accessible to a first years student in mathematics. The topics discussed here are basic tropical algebra, tropical plane curves, some tropical intersections, and Viro's patchworking.…
Tropical algebraic geometry is an active new field of mathematics that establishes and studies some very general principles to translate algebro-geometric problems into purely combinatorial ones. This expository paper gives an introduction…
We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.
Complex algebraic varieties become easy piecewise-linear objects after passing to the so-called tropical limit. Geometry of these limiting objects is known as tropical geometry. In this short survey we take a look at motivation and…
The paper consists of lecture notes for a mini-course given by the authors at the G\"okova Geometry \& Topology conference in May 2014. We start the exposition with tropical curves in the plane and their applications to problems in…
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.
Tropical algebraic geometry offers new tools for elimination theory and implicitization. We determine the tropicalization of the image of a subvariety of an algebraic torus under any homomorphism from that torus to another torus.
We study some topological properties of attractors.
The notion of geometric construction is introduced. This notion allows to compare incidence configurations in the algebraic and tropical plane. We provide an algorithm such that, given a tropical instance of a geometric construction, it…
This is a guide on how to create 3d printable models of tropical surfaces, curves, and combinations thereof. It uses Polymake to construct bounded models of the tropical objects, and OpenSCAD to thicken and export them to any common 3D…
We study topological properties of the graph topology.