An invitation to the algebraic geometry over idempotent semirings - Lecture 1

Speaker: Cristhian Garay

Date: Mon, Feb 6, 2023

Location: PIMS, University of Lethbridge, Online, Zoom

Conference: Mini-course in algebraic geometry over idempotent semirings

Subject: Mathematics, Number Theory

Class: Scientific


Idempotent semi-rings have been relevant in several branches of applied mathematics, like formal languages and combinatorial optimization.

They were brought recently to pure mathematics thanks to its link with tropical geometry, which is a relatively new branch of mathematics that has been useful in solving some problems and conjectures in classical algebraic geometry.

However, up to now we do not have a proper algebraic formalization of what could be called “Tropical Algebraic Geometry”, which is expected to be the geometry arising from idempotent semi-rings.

In this mini-course we aim to motivate the necessity for such theory, and we recast some old constructions in order theory in terms of commutative algebra of semi-rings and modules over them.


This lecture is the first part of a mini-course, please see also