Registration Number
0126U001859,
R & D request
Title
Modern methods of analysis of analytical and asymptotic aspects of problems in geometry and mathematical physics
Head
Dmytro H. Shepelskyi, Доктор фізико-математичних наук
Registration Date
12-02-2026
Organization
B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine
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The aim of the work is to develop analytical, asymptotic, topological, and numerical methods for solving problems in geometry and mathematical physics that are relevant both in terms of the development of fundamental research and potential applications in mathematical modeling of complex physical and biological processes and in solving urgent problems in data analysis, cryptography, and computer graphics. Within the framework of modern differential geometry and the theory of integrable systems, it is planned to develop a geometric and analytical theory of multidimensional pseudo-spherical submanifolds and their Bianchi-Beklund-type transformations. A homogenization theory for differential equations on Riemannian manifolds of complex microstructure will be constructed, and the asymptotic behavior of harmonic differential forms on manifolds whose topological genus grows indefinitely with appropriately coordinated behavior of the manifold metric will be described. We plan to study the asymptotic behavior of solutions to spectral problems for nonlocal operators of the convolution type in the limit of small characteristic interaction length.
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2026-02-12
