Since the 6th Workshop in 2018, we witnessed a rapid development in the field of combinatorial methods in application to geometry and mathematical physics. We are observing inter-proliferation of two main subjects traditionally presented in the workshop agenda—cluster algebras and topological recursion. It is tempting to see how these two topics can be unified within the mirror symmetry framework, how spectral curves obtained from Landau-Ginzburg potentials motivated by cluster algebras can arise within the classical and quantum topological recursion, and how it all can be interpreted in cohomological field theory framework and be applied to knot theory and knot invariants. Notable is also a modern development of cluster structures in Lie algebras, including classical and quantum algebras of monodromies of Fuchsian systems, and other fascinating topics related to clusters and topological recursion including a modern treatise of Masur–Veech volumes.

Financial support. The conference 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).

Program

Abstracts

Program Committee
Chekhov Leonid Olegovich
Fomin Sergei Vladimirovich
Lando Sergei Konstantinovich
Marshakov Andrei Vladimirovich
Mazzocco Marta
Orlov Dmitri Olegovich

Organizing Committee
Chekhov Leonid Olegovich
Korotkin Dmitrii Aleksandrovich
Krichever Igor Moiseevich
Lando Sergei Konstantinovich
Nechaev Sergei Konstantinovich
Sergeev Armen Glebovich
Zograf Petr Georgievich

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
National Research University Higher School of Economics, Moscow
Skolkovo Institute of Science and Technology
Steklov International Mathematical Center