The seminar is devoted to the analysis of other authors' work on the theory of three- and four-dimensional manifolds and knot theory published in recent years, as well as some classical works that remain relevant. The focus is on algorithmic issues, the theory of codimension-one foliations, contact topology, homological invariants, concordance groups of links and three-dimensional homological cobordism, smooth structures on four-dimensional manifolds, and other relevant topics.

The following topics are planned for discussion in the fall semester of the 2025/2026 academic year.

• Bernstein and Wang's work on low-entropy hypersurfaces in four-dimensional Euclidean space.
• The work of Balmer and Kleiner on the contractibility of the group of diffeomorphisms onto the group of isometries of a three-dimensional closed manifold of constant non-zero curvature.
• Brittenham and Hermiller's result on the strict subadditivity of the Gordian number.
• Lidman and Piccirillo's work on a new distinction of smooth structures on four-dimensional manifolds using smooth knot truncation.
• The work of Gabai, Gay and Hartman on the construction of exotic diffeomorphisms of the three-dimensional sphere.

Seminar organizers
Dynnikov Ivan Alekseevich
Prasolov Maxim Vyacheslavovich
Shastin Vladimir Alekseevich

Financial support
The seminar is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, agreement no. 075-15-2025-303).

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