Tropical geometry in higher rank

Abstract: A valuation The link between algebraic geometry and tropical geometry is given by a valuation from the field to the real numbers. A valuation over the reals is a valuation of rank one. In commutative algebra valuations are defined over totally ordered groups. The tropical semiring is the semiring ${\displaystyle (\mathbb{R} \cup \{+\infty \},\oplus ,\otimes)}$, with the operations $x\oplus y=\min\{x,y\}, x\otimes y=x+y$. These operations may be defined for any totally ordered group G. What is the notion of convexity in $G^n$? Are the tropical varieties easy to describe?

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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