Symmetries in algebraic and topological structures on infinite-dimensional analytic manifolds and their possible applications

Project registration number: 2020.02/0025
Project duration: from 2020 to 2022.
The total cost of the project: UAH 7,415,000 thousand.
Name of the competition:
NFSU competition “Supporting the research of leading and young scientists”

The goal of the project:

The goal of the project is to establish the properties of the spectra (and their subsets) of the algebras of S-invariant analytic functions of bounded type on the Banach space X for different symmetry semigroups S and spaces X. In particular, we are interested in the existence of the structure of an analytic manifold on the spectrum or some of its subsets, the existence of natural algebraic structures related to the action of the semigroup S, a description of the differentiations of this algebra using spectrum elements. Specific algebras of symmetric, block-symmetric, and supersymmetric analytic functions with respect to discrete and continuous symmetry semigroups will be considered. Also, the case of algebras of real analytic functions on real Banach spaces will be considered. In addition, the obtained results will be generalized for algebras of analytic functions on the Banach space, which are generated by a countable family of polynomials. Based on the obtained results, new approaches for creating public key encryption algorithms, constructing pseudorandom generators, pattern recognition algorithms, and creating new mathematical tools for modeling quantum mechanics processes will be proposed.

Contact person and project manager at the Vasyl Stefanyk Precarpathian National University: Doctor of Physical and Mathematical Sciences, Professor, Head of the Department of Mathematical and Functional Analysis Andriy Vasyliovych Zagorodnyuk,