Continuous structurally fractal functions defined in terms of the $Q_s$-representation and nega-$Q_s$-representation of numbers (Ph.D. student's report)

Abstract: The Ph.D. student will report on his progress in completing the individual plan of study as well as the education and research program. This event is open, i.e., everyone is welcome to join the seminar and participate in the discussion.

His research lies on the border of the constructive theory of functions with locally complicated structure and fractal properties, theory of encoding of real numbers, metric and probabilistic number theory. The dissertation focuses on the applications of finite-symbol representations of real numbers with zero redundancy, such as the $Q_s$-representation and nega-$Q_s$-representation, in the constructive theory of functions with structurally fractal properties defined on the interval $[0, 1]$.

Ukrainianclassical analysis and ODEsfunctional analysisnumber theory

Audience: researchers in the discipline

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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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