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THE MASLOVDEQUANTIZATION,TROPICALMATHEMATICS, IDEMPOTENT
MATHEMATICS, AND GEOMETRY
G. Litvinov
(Independent University of Moscow, Russia)
Email address: [email protected]
Tropical mathematics is a part of idempotent mathematics. Tropical algebraic geometry can be treated as aresult of the Maslov dequantization applied to the traditional algebraic geometry (O. Viro, G. Mikhalkin).There are interesting relations and applications to thetraditional convex geometry.
In the spirit of N.Bohr's correspondence principle thereis a (heuristic) correspondence between important, useful, and interesting constructions and results over fieldsand similar results over idempotent semirings. A systematic application of this correspondence principle leadsto a variety of theoretical and applied results.
The Maslov dequantization
Semirings and semifields
Idempotent analysis
The superposition principle and linear problems
Convolution and the Fourier–Legendre transform
Idempotent functional analysis
The dequantization transform
Dequantization of set functions on metric
spaces
Dequantization of geometry