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

Комбинаторика пространств модулей, кластерные алгебры и топологическая рекурсия = Combinatorics of Moduli Spaces, Cluster Algebras and Topological Recursion : материалы VII Международного семинара (31 мая–4 июня 2021 г., ВШЭ, МИАН, Сколтех, г. Москва) / Математический институт им. В.А. Стеклова Российской академии наук [и др.]. – Москва, 2021.