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An invitation to tropical geometry
Evolutionary and Institutional Economics Review, 2015Applications of tropical geometry to various problems in economics emerged recently and gained a considerable amount of attention. This article provides a gentle introduction to the notions and techniques of tropical geometry for the mathematically inclined reader.
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Oberwolfach Reports, 2023
The workshop "Tropical methods in geometry" was devoted to a wide discussion and exchange of ideas between the leading experts representing various points of view on the subject including tropical methods in symplectic and Lagrangian geometry, topology of real algebraic varieties and tropical homology, tropical methods in algebraic, Berkovich analytic ...
Ilia Itenberg +3 more
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The workshop "Tropical methods in geometry" was devoted to a wide discussion and exchange of ideas between the leading experts representing various points of view on the subject including tropical methods in symplectic and Lagrangian geometry, topology of real algebraic varieties and tropical homology, tropical methods in algebraic, Berkovich analytic ...
Ilia Itenberg +3 more
+4 more sources
2018
What kind of strange spaces hide behind the enigmatic name of tropical geometry? In the tropics, just as in other geometries, one of the simplest objects is a line. Therefore, we begin our exploration by considering tropical lines. Afterwards, we take a look at tropical arithmetic and algebra, and describe how to define tropical curves using tropical ...
Brugallé, Erwan +3 more
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What kind of strange spaces hide behind the enigmatic name of tropical geometry? In the tropics, just as in other geometries, one of the simplest objects is a line. Therefore, we begin our exploration by considering tropical lines. Afterwards, we take a look at tropical arithmetic and algebra, and describe how to define tropical curves using tropical ...
Brugallé, Erwan +3 more
openaire +2 more sources
Oberwolfach Reports, 2008
This is the first appearance of “Tropical Geometry” as the topic of an Oberwolfach workshop, though the subject figured earlier at the Forschungsinstitut as an Oberwolfach Seminar on “Tropical Algebraic Geometry” in October 2004. The workshop was organized by Eva-Maria Feichtner (U Bremen), Andreas Gathmann (U Kaiserslautern), Ilia Itenberg (U ...
Eva Maria Feichtner +3 more
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This is the first appearance of “Tropical Geometry” as the topic of an Oberwolfach workshop, though the subject figured earlier at the Forschungsinstitut as an Oberwolfach Seminar on “Tropical Algebraic Geometry” in October 2004. The workshop was organized by Eva-Maria Feichtner (U Bremen), Andreas Gathmann (U Kaiserslautern), Ilia Itenberg (U ...
Eva Maria Feichtner +3 more
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2007
Tropical Geometry is a new and rapidly developing discipline that touches upon many branches of modern mathematics. It is characterized by the transition of algebro-geometric objects to piecewise-linear ones, thereby retaining much of the algebro-geometric data while unveiling novel sets of techniques for outstanding problems.
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Tropical Geometry is a new and rapidly developing discipline that touches upon many branches of modern mathematics. It is characterized by the transition of algebro-geometric objects to piecewise-linear ones, thereby retaining much of the algebro-geometric data while unveiling novel sets of techniques for outstanding problems.
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What Tropical Geometry Tells Us about the Complexity of Linear Programming
SIAM Review, 2021Xavier Allamigeon +2 more
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Parametric Shortest-Path Algorithms via Tropical Geometry
Mathematics of Operations Research, 2022Michael Joswig, Benjamin Schröter
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Computer Algebra Methods in Tropical Geometry
2010Tropical geometry is a young field of mathematics which allows to study properties of objects from algebraic geometry with the aid of methods from discrete mathematics, like convex geometry and combinatorics. There are different ways to introduce tropical varieties and to derive the connection between these and their algebraic counterparts.We use a way,
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Tropical analytic geometry, Newton polygons, and tropical intersections
Advances in Mathematics, 2012Joseph Rabinoff
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