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

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