17 Sep 2008; Mat-Nat Faculty (UiTø), room A228. Wednesday 10:15-12:00

Grigory L. Litvinov (Independent university of Moscow)

"The Maslov dequantization and tropical mathematics".

Tropical mathematics can be treated as a result of a dequantization of the traditional mathematics as the Planck constant tends to zero taking imaginary values. This kind of dequantization is known as the
Maslov dequantization and it leads to a mathematics over tropical algebras like the max-plus algebra. The so-called idempotent dequantization is a generalization of the Maslov dequantization.

The idempotent dequantization leads to idempotent mathematics over idempotent semi-rings. For example, the field of real or complex numbers can be treated as a quantum object whereas idempotent semi-rings can be examined as "classical" or "semi-classical" objects (a semi-ring is called idempotent if the semi-ring addition is idempotent, i.e. x+x=x).

In the spirit of N.Bohr's correspondence principle there is a (heuristic) correspondence between important, useful and interesting constructions and results over fields and similar results over idempotent semi-rings. A systematic application of this correspondence principle leads to a variety of theoretical and applied results.