Maxim Kontsevich: What is tropical mathematics? [2013]

Slides for this talk:
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Maxim Kontsevich
October 15, 2013
What is tropical mathematics?
In tropical mathematics the usual laws of algebra are changed, the subtraction is forbidden, the division is always permitted, and 1+1 is equal to 1. Analogs of usual geometric shapes like lines, circles etc. are replaced by new figures composed of pieces of lines. I will try to explain basics of tropical algebra and geometry, its relation with more traditional domains, and its role in mirror symmetry which is a remarkable duality originally discovered in string theory about 20 years ago.
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