abstract: I will discuss several constructions one can perform starting from a list of vectors and show how some ideas coming from the theory of hyperplane arrangements come into play in numerical analysis and arithmetic. The material is based on a forthcoming book with De Concini, preliminary version available at www.mat.uniroma1.it~procesidida.html: Hyperplane arrangements, polytopes, box-splines.
Procesi-minicourse-lecture1