12:00-12:20 Uhr Lehrprobe zum Thema The Theorem of Carathéodory (auf Englisch)

ca. 12:30-13:10 Uhr Fachvortrag:

Polytopes meet polynomials: realization spaces and tropical varieties

Many exciting research topics lie at the interface between discrete, tropical, and algebraic geometry.
In this talk I will present examples of such topics based on some of my research projects.
The first part introduces the study of algebraic degrees of realizations of polytopes satisfying some geometric constraints. The second one focuses on the analysis through the lens of tropical geometry of models of cubic surfaces, matroid polytopes, and their subdivisions. Throughout the talk, I will highlight how discrete and algebraic methods fruitfully interact and provide new insights and computational tools.