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Tropical Geometry

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.
openaire   +2 more sources

Homological Mirror Symmetry and Tropical Geometry

Lecture Notes of the Unione Matematica Italiana, 2014
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry.
Pantev, Tony, Soibelman, Yan, Catanese, Fabrizio, Zharkov, Ilia, Castano-Bernard, Ricardo, Kontsevich, Maxim   +5 more
exaly   +2 more sources

Geometric Capacity of Transformers: A Tropical Geometry Perspective

To quantify the geometric capacity of transformers, we develop a tropical-geometric framework for analyzing the spatial partitions induced by conditioned self-attention. In the zero-temperature limit, we show that fixed-key top-$1$ routing is exactly represented by a power diagram in query space, while an auxiliary log-lifted value parameterization ...
Su, Ye, Liu, Yong
openaire   +1 more source

What Tropical Geometry Tells Us about the Complexity of Linear Programming

SIAM Review, 2021
Allamigeon Xavier, Stéphane Gaubert, Michael Joswig   +2 more
exaly  

On the Decision Boundaries of Neural Networks: A Tropical Geometry Perspective

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023
Bernard Ghanem, Adel Bibi, Motasem Alfarra   +2 more
exaly  

Parametric Shortest-Path Algorithms via Tropical Geometry

Mathematics of Operations Research, 2022
Michael Joswig, Benjamin Frederik Schröter   +1 more
exaly  

Tropical analytic geometry, Newton polygons, and tropical intersections

Advances in Mathematics, 2012
Joseph Rabinoff
exaly  

Mirror symmetry for and tropical geometry

Advances in Mathematics, 2010
Mark Gross
exaly  

Algebraic, tropical, and fuzzy geometry

Beitrage Zur Algebra Und Geometrie, 2011
Walter W. Wenzel, Andreas W M Dress
exaly  

Incidence geometry and universality in the tropical plane

Journal of Combinatorial Theory - Series A, 2018
Dhruv Ranganathan
exaly