Branching processes are one of the most interesting parts of probability theory. Originated in the middle of the 19th century as a theory that tried to explain the causes of the extinction of famous surnames in the UK, the theory of branching processes has now become a very extensive field of probability theory and a powerful research tool in various fields of mathematics, such as algorithm theory, queuing theory, random mapping theory, percolation theory, as well as in many sections of other sciences, including physics, chemistry, biology and demography.

Within the framework of a one semester course, it is difficult to present even the most important results of the theory of branching processes, not to mention its applications. Therefore, only the following sections will be included in the course:

1. Galton-Watson processes, classification, limit theorems for subcritical, critical and supercritical processes. PCR-test. Connection of Galton-Watson processes with random walks. Galton-Watson processes and First-In-First-Out (FIFO) queuing systems.
2. Reduced processes. The distance to the most recent common ancestor.
3. Markov branching processes, classification, limit theorems, regularity. Branching processes with immigration.
4. Branching processes with the final product. Queuing systems with one server, infinite queue capacity and service in random order (SIRO). Branching processes with immigration and the final product. Queueing systems with repeated calls.

Please, address Vladimir Vatutin, vatutin@mi-ras.ru, for Zoom data.

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).

Lecturer
Vatutin Vladimir Alekseevich

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