Results 11 to 20 of about 84,678 (251)
A bit of tropical geometry [PDF]
The American Mathematical Monthly, 2014 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 patchworking.
Brugallé, Erwan, Shaw, Kristin
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Intersecting Solitons, Amoeba and Tropical Geometry [PDF]
Physical Review D, 2008 We study generic intersection (or web) of vortices with instantons inside, which is a 1/4 BPS state in the Higgs phase of five-dimensional N=1 supersymmetric U(Nc) gauge theory on R_t \times (C^\ast)^2 \simeq R^{2,1} \times T^2 with Nf=Nc Higgs scalars ...
A. A. Abrikosov +25 more
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Tropical geometry of Rado matroids [PDF]
Discrete Mathematics LettersIn this note, we characterize the products of simplicial generators for the Chow ring of a loopless matroid, extending a result of Backman, Eur, and Simpson. We prove that the stable intersection of a collection of tropical hyperplanes centered at the origin with the Bergman fan of a matroid is the Bergman fan of the dual of a certain Rado matroid.
Calum Buchanan, Richard Danner
doaj +3 more sources
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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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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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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Hokkaido Mathematical Journal, 2009 The construction of a tropical hypersurface is given by modeling the classical construction of a complex hypersurface. A tropical meromorphic function of finite type is shown to be a tropical rational function. One also has tropical nullstellensatz.
Illia Itenberg +2 more
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Geometry in the tropical limit [PDF]
Mathematische Semesterberichte, 2011 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 intuition behind this limit and consider a few simple examples of correspondence principle between classical and tropical ...
Itenberg Ilia, Mikhalkin Grigory
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Estimates of tropical cyclone geometry parameters based on best-track data [PDF]
Natural Hazards and Earth System Sciences, 2019 Parametric wind profiles are commonly applied in a number of engineering applications for the generation of tropical cyclone (TC) wind and pressure fields.
K. Nederhoff +3 more
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A MODULI STACK OF TROPICAL CURVES
Forum of Mathematics, Sigma, 2020 We contribute to the foundations of tropical geometry with a view toward formulating tropical moduli problems, and with the moduli space of curves as our main example.
RENZO CAVALIERI +3 more
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