The special course is intended for a wide audience and is available to first-year students. It will present the main results of the lecturer on the theory of multidimensional Peano curves, including the solution of Arnold's problem on the Hölder mapping of a square onto a cube.

Program.

1. Fractals and fractal curves.
2. Hausdorff and asymptotic dimension and measure.
3. Dimension-raising Hölder mappings.
4. The theorems of stabilization of Hölder ratio.
5. Arnold's problem of the Hölder mapping of a square onto a cube.
6. Variations and hypervariations of curves and compacts.
7. The Kakutani-Gomori problem about the «length of a square».
8. Continuous-discrete duality.
9. The digital plane.
10. Computer applications of fractals.

Lecturer
Shchepin Evgeny Vital'evich

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