Results 11 to 20 of about 1,478,276 (282)
Tropical geometry over the tropical hyperfield [PDF]
Rocky Mountain Journal of Mathematics, 2022 In this text, we merge ideas around the tropical hyperfield with the theory of ordered blueprints to give a new formulation of tropical scheme theory. The key insight is that a nonarchimedean absolute value can be considered as a morphism into the tropical hyperfield.
Lorscheid, O. ; https://orcid.org/ +1 more
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Introduction to Tropical Geometry
, 2015 Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum ...
Maclagan, D., Sturmfels, B.
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Phylogenetic trees and the tropical geometry of flag varieties [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We will discuss some recent theorems relating the space of weighted phylogenetic trees to the tropical varieties of each flag variety of type A. We will also discuss the tropicalizations of the functions corresponding to semi-standard tableaux, in ...
Christopher Manon
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Tropical geometry of statistical models [PDF]
Proceedings of the National Academy of Sciences, 2004 This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific ...
Pachter, Lior, Sturmfels, Bernd
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Tropical Oriented Matroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Tropical oriented matroids were defined by Ardila and Develin in 2007. They are a tropical analogue of classical oriented matroids in the sense that they encode the properties of the types of points in an arrangement of tropical hyperplanes – in much the
Silke Horn
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Lefschetz (1,1)-theorem in tropical geometry [PDF]
Épijournal de Géométrie Algébrique, 2018 For a tropical manifold of dimension n we show that the tropical homology classes of degree (n-1, n-1) which arise as fundamental classes of tropical cycles are precisely those in the kernel of the eigenwave map.
Philipp Jell, Johannes Rau, Kristin Shaw
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Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We study the combinatorics of weighted trees from the point of view of tropical algebraic geometry and tropical linear spaces. The set of dissimilarity vectors of weighted trees is contained in the tropical Grassmannian, so we describe here the tropical ...
Benjamin Iriarte Giraldo
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Algebraic singularities of scattering amplitudes from tropical geometry
Journal of High Energy Physics, 2021 We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar N $$ \mathcal{N} $$ = 4 super Yang-Mills theory.
James Drummond +3 more
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Pattern Formation and Tropical Geometry
Frontiers in Physics, 2020 Sandpile models exhibit fascinating pattern structures: patches, characterized by quadratic functions, and line-shaped patterns (also called solitons, webs, or linear defects).
Nikita Kalinin, Nikita Kalinin
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On Rational Equivalence in Tropical Geometry [PDF]
Canadian Journal of Mathematics, 2016 AbstractThis article discusses the concept of rational equivalence in tropical geometry (and replaces an older, imperfect version). We give the basic definitions in the context of tropical varieties without boundary points and prove some basic properties.
Allermann, Lars +2 more
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