Polynomials in min-plus algebra and related algorithmic problems

A min-plus semiring is a set of real numbers, possibly with infinity, endowed with two operations: tropical addition, which is just usual minimum operation, and tropical multiplication, which is usual addition. Polynomials in this semiring can be defined analogously to classical polynomials. In this talk we will review some recent results on min-plus polynomials including studies of systems of min-plus linear polynomials and a min-plus analog of Hilbert’s Nullstellensatz.