"Tropical Mathematics" by Sandra Spiroff
 

Document Type

Lecture

Publication Date

8-25-2016

Abstract

The adjective 'tropical' arises simply from the French view of Brazil in the 1980s and 1990s; the mathematical theory would more aptly be described as min-plus algebra. Our particular interest is the tropical semiring, whose objects are real numbers, along with positive infinity, and whose two binary operations are defined to be the minimum and the sum. We aim to generalize this definition to higher dimensions. Our objects are closed convex sets in real n-space, with a fixed recession cone, and operations defined to be the closed convex hull and the Minkowski sum. In the case of dimension one, this reduces to the original definition. (This talk is accessible to graduate students.)

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