Abstract:
Suppose that we replace the usual operations of addition
and multiplication of real numbers by the following "tropical" operations:
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the tropical sum of a and b is min{a,b}
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the tropical product of a and b is a+b.
Tropical polynomials are piecewise-linear functions.
For example, the tropical version of the polynomial
x2+x+2 is the function f(x)=min{2x,1+x,2}.
Tropical methods have been used to solve problems in many
areas of mathematics by passing to piecewise-linear
models. This talk will focus on the basics of tropical
algebra and will be at an elementary level.