Generic chaining is a powerful modern tool for obtaining upper bounds for the expectation of the maximum of a random process. The basic idea of chaining first appeared in Kolmogorov's proof of the already classical theorem on the continuity of the trajectories of a random process under Kolomogorov's assumptions. Modern applications of the generic chaining reach far beyond the theory of stochastic processes. In particular, chaining technique has applications in the geometry of finite dimensional Banach spaces.

Within the framework of the course we will, first, get acquainted with the main ideas and methods of the generic chaining. Secondly, we will study possible applications of the technique to the problem of the embedding of $N$-dimensional subspaces of $L_p[0, 1]$ into finite dimensional spaces $\ell_p^{m(N)}$.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2022-265).

Program

Lecturer
Kosov Egor Dmitrievich

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center