The theory of dessins d'enfants will be presented as a trilingual vocabulary (combinatorial topology, arithmetic geometry, finite transformation groups). We shall present a proof of the Belyi theorem, allowing to "draw" any curve over any number field. The relations with the theory of modular curves will be established as well as with various problems of number theory, including some generalized Fermat equations.

Просьба к участникам обращаться к Георгию Борисовичу Шабату, george.shabat@gmail.com, 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
Shabat Georgii Borisovich

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