Lara Bossinger
Title: Towards a fundamental theorem for totally positive tropical geometry
Abstract: The fundamental Theorem of (algebraic) tropical geometry states that three different approaches to Tropicalization yield the same tropical variety. However, the different notions of tropicalzation treated in the theorem are not exhaustive: for schemes with a positive atlas Fock and Goncharov introduced another tropicalzation as functor of points over a semi field. In this talk I will explain Fock—Goncharov’s tropicalization and show that it fits into a positive analogue of the fundamental theorem extending results of Speyer and Williams. The result holds for cluster varieties of finite type that arise naturally in this context. The talk is based on results in arxiv:2208.01723.