High-dimensional analysis and probability

Breve orale + Relazione di seminario

• -classical convexity theory: Hahn-Banach, Caratheodory, Helly, Radon, Brunn-Minkowski, Prekopa-Leindler, John's ellipsoid...; 
• -concentration of measure phenomenon: geometric and functional version, Khintchine's inequality..;
• -theorems of Johnson-Lindenstrauss and Dvoretzky; 
• -selected topics (depending on time and interest): sphere packing, combinatorial optimization problems in high dimension...

• Schneider Convex Bodies: the Brunn-Minkowski Theory; 
• Ball An Elementary Introduction to Modern Convex Geometry; 
• Vershynin High-Dimensional Probability: An Introduction with Applications in Data Science; 
• Artstein-Avidan, Giannopoulos, Milman Asymptotic Geometric Analysis, Part I and II;