High-dimensional analysis and probability
Programma
- -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...
Obiettivi formativi
By the end of the course, the student will become familiar with phenomena and tools in analysis and probability in high dimensions, and will be able to understand and to present in a clear and independent way contemporary results in this topic.
Riferimenti bibliografici
- 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;