Approximation theory studies methods and limits of approximation of various objects (e.g. functions) by simpler objects (e.g. polynomials). One of the goals of our course is to give an introduction into this branch of mathematics.

To prove that it is impossible to obtain a good apprixmation one has to show that the approximated object is sufficiently "large" or "complex". Here approximation theory is connected with complexity theory from Computer Science. The second goal of our course is to show some links between these theories on specific examples. We will consider several measures of complexity of matrices (rigidity, approximation rank, signum rank) that came from complexity theory and their application to problems of approximation.

Просьба к участникам обращаться к Юрию Вячеславовичу Малыхину, malykhin@mi-ras.ru, за данными для подключения к занятиям через Zoom.

Financial support. The course is supported by the Simons Foundation and the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

Lecturer
Malykhin Yuri Viatcheslavovich

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