The role of Academician Volodymyr Korolyuk in the development of fractal analysis in Ukraine

Abstract: Volodymyr Semenovych Korolyuk (August 19, 1925 – April 4, 2020) was a prominent Ukrainian scientist specializing in probability theory, mathematical statistics, and cybernetics. He was a Doctor of Physical and Mathematical Sciences (1963), Professor (1964), and Academician of the National Academy of Sciences of Ukraine (1976).

In the talk, we briefly describe his biography as well as academic and organizational achievements. The main part of the talk is devoted to Academician Korolyuk's impact on the initiation and development of fractal analysis as a field of mathematics in Ukraine.

Ukrainianclassical analysis and ODEsdynamical systemsfunctional analysishistory and overviewnumber theoryprobability

Audience: general audience

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Семінар з фрактального аналізу / Fractal analysis seminar

Series comments: Weekly research seminar on fractal analysis (online)

Topics:

• theory of fractals (fractal geometry and fractal analysis)
• Hausdorff–Besicovitch dimension, techniques and methods for its calculation and estimation
• functions and transformations preserving fractal (Hausdorff–Besicovitch, entropic, box-counting, packing, etc.) dimension
• sets of metric spaces that are essential for functions, sets, and dynamical systems
• self-similar, self-affine properties of mathematical objects
• systems of encoding for real numbers (numeral systems) and their applications
• metric number theory and metric theory of representations of numbers
• probabilistic number theory and probabilistic theory of representations of numbers
• measures supported on fractals, particularly singular measures and probability distributions
• nowhere monotonic and nowhere differentiable functions, functions with fractal properties
• theory of groups determined by invariants of transformations preserving tails of representation of numbers, digit frequencies, etc.

The talks are mostly in Ukrainian but English is also acceptable

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