The theory of symmetric functions has many applications in various fields of mathematics, for example, in combinatorics, algebraic geometry, representation theory and mathematical physics. Macdonald polynomials are polynomials with two parameters, which generalize various well-known classes of symmetric polynomials. Macdonald symmetric functions are still of great interest. Many properties of symmetric polynomials can be better understood with the help of operators acting on them. In the case of Macdonald polynomials these are difference operators commuting among themselves. Bright examples of many-body integrable systems (such as Calogero system and its relativistic analogue Ruijsenaars system) are directly related to the theory of Macdonald operators and symmetric functions.

Please, address Mariya Matushko, matushko@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
Matushko Mariya Georgievna

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