The main research objects in this project are the geometric properties of fractal sets and measures. A special attention is paid to fractals that arise as limits in natural random processes. Fractals are irregular mathematical objects having very different fine structure compared to smooth objects such as regular curves or surfaces. The classical methods of mathematical analysis are not suited in studying properties of such fractals. As many phenomena in the nature can be modeled as random fractals, it is very important to develop mathematical machinery for their investigation. The results will have applications in geometric measure theory, fractal geometry, harmonic analysis, geometric analysis, and game theory.

2025

2029