Title: Positive tropicalization and its applications
Abstract: Tropical geometry builds a bridge between algebraic and polyhedral geometry by transforming an algebraic variety into a polyhedral object that preserves key properties of the original variety. Recently, there has been increasing interest in the tropicalization of the positive part of algebraic varieties, and more generally, in the tropicalization of semi-algebraic sets.
In this talk, we present real analogues of the Fundamental Theorem of Tropical Geometry in the context of positive tropicalization. Building on these results, we explore the geometric stability of semi-algebraic sets and present an algorithm that provides lower bounds on the maximal number of positive real solutions of a parametrized polynomial system. This talk is based on joint works with Lorenzo Baldi and Kemal Rose.
The advanced seminar begins at 4:00 pm s.t..