Analytical and Probabilistic Methods in the Geometry of Convex Bodies
IM PAN Lecture Notes, Vol. 2, Warsaw 2014, ISBN: 978-83-86806-24-9
Olivier Guedon, Piotr Nayar and Tomasz Tkocz, Concentration inequalities and geometry of convex bodies, 9-86
Dmitry Ryabogin and Artem Zvavitch, Analytic methods in convex geometry, 87-183
About the book:
The study of finite-dimensional Banach spaces and high-dimensional convex bodies has become a natural counterpart and complement to the classical functional analysis. Some powerful methods have been invented for this purpose since the 1970s, and many of them involve the ingenious use of probabilistic or functional inequalities. This book contains two series of lecture notes. The first of them explores the wide family of concentration inequalities and the way in which they can be applied in the geometry of convex bodies, while the second one discusses the notion of duality and tools coming from harmonic analysis. They lead the reader from classical results to recent advances in the subject.
About the author:
Olivier Guedon is a Professor at Laboratoire d'Analyse et de Mathematiques Appliquees of Universite Paris-Est Marne-la-Vallee. His research covers many branches of analysis and probability, in particular applications of probabilistic methods in convex geometry and local theory of Banach spaces. Piotr Nayar and Tomasz Tkocz are mathematics PhD students at the University of Warsaw and University of Warwick, respectively. They are interested in various topics in analysis, probability and convex geometry. Dmitry Ryabogin and Artem Zvavitch are Associate Professors at the Department of Mathematical Sciences of Kent State University. Research interests of Dmitry Ryabogin include harmonic analysis and its interplay with convex and integral geometry. Artem Zvavitch specializes in applications of harmonic analysis and probability theory to convex geometry and geometric functional analysis.