Knot theory is a rapidly developing branch of geometry and topology. Modern knot theory is characterized by a combination of methods of low-dimensional topology, algebraic topology, combinatorics, representation theory, group theory, geometry of spaces of constant curvature. Many of the known methods for studying knots in a three-dimensional sphere were further generalized and used to study knots in thickened surfaces and other three-dimensional manifolds, to study notoids and knotted graphs.
The conference is expected to discuss new results and open problems related to the study of algebraic structures associated with knots and their generalizations; the study of geometric invariants of geometric structures arising on complements of knots and links.
The main directions of the scientific program:
- Algebraic structures in knot theory.
- Hyperbolic knots and their invariants.
- Volumes of hyperbolic manifolds and polyhedra.
- Applications of knot theory.
The scientific program of the conference will include invited talks and contributed presentations.