Bi-annual Algebraic and Tropical Meetings of
Brown and YaLE
(BATMOBYLE)

Semialgebraic sets are those defined by polynomial inequalities over an algebraically closed field. In this talk I will discuss their tropicalization and analytification. We show that the real analytification is homeomorphic to the inverse limit of real tropicalizations, analogously to a result of Payne. We also show a real analogous of the fundamental theorem of tropical geometry. The talk will be accessible to graduate students with background on basic algebraic geometry. This is based on joint work with Philipp Jell and Claus Scheiderer.