This school will introduce participants to knot theory and geometric topology. The talks are geared towards bachelor and master students and they will require only minimal previous knowledge of topology. The lecture courses will present many exercises and problems for the students to work on during the week.

Applications of links, braids, and diffeomorphisms of surfaces play a key role in many areas of mathematics, physics, chemistry, biology, cryptography, and other natural sciences.

In turn, algebraic and homotopy properties of diffeomorphisms of surfaces are necessary for understanding the structure of 3- and 4-manifolds. They are also important in almost all parts of mathematics related with geometrical and topological analysis, including dynamical systems, mathematical physics, PDE, complex analysis, number theory etc.

The lecturers will help the students with the exercise problems, and they will also provide guidance for the students to go into research problems.

Necessary prerequisites: The students are assumed to have a basic knowledge in general, algebraic and differential topology. In particular, one should know most of the following notions:

• General topology: topological spaces, compactness, connectedness;

• Preferably, but not mandatory:

• Algebraic topology: fundamental group, covering spaces;

• Differential topology: a notion of a manifold.

The application form will be open shortly.