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Nonlocal boundary value problems: index theory and semiclassical asymptotics

Project leader

Anton Savin

Department

S.M. Nikol’skii Mathematical Institute

Tags

nonlocal boundary value problems special domains Fredholm operators ellipticity of the index formula noncommutative geometry semiclassical asymptotics Lagrangian manifolds
Mathematics and Telecommunications Differential Equations
Functional-analytical methods for the study of boundary value problems for differential and functional differential equations with partial derivatives

Project leader

Vitalii Volpert

The main idea of the project: research of new classes of differential and functional-differential equations, inequalities and systems and the application of the obtained results to interdisciplinary research in mathematical models of physical and biological processes.

Department

S.M. Nikol’skii Mathematical Institute

Tags

reaction-diffusion equations Vlasov equation Liouville equation difference schemes identification problems for mixed partial differential equations elliptic functional differential equation nonlocal terms quasilinear equations differential-difference equations nonlocal elliptic operators Fredholm property index absolutely continuous spectrum singular spectrum scattering matrix trace formulas
Mathematics and Telecommunications Differential Equations
Non-commutative elliptic theory for the actions of groups on manifolds

Project leader

Anton Savin

The project aims to explore a number of interconnected challenges of modern theory of elliptic operators on manifolds with the actions of groups.

Department

S.M. Nikol’skii Mathematical Institute

Tags

elliptic theory Fredholm index noncommutative geometry quantized canonical transformations relative elliptic theory manifolds with singularities Sobolev problems algebraic index theorems
Mathematics and Telecommunications Telecommunication systems
Creation of Laboratory for Advanced Research in 5G Internet of Things wireless networks

Project leader

Konstantin Samouylov

Set up a world-class Research Center for solving practical problems in 5G wireless networks in regard to the network technologies and conducting experimental studies

Department

Applied Mathematics & Communications Technology Institute

Tags

Internet of Things mobility interference efficiency index quality of service indicators random process Markov process motion model random walk nonuniform, sources of information limited resources probability- time-response characteristics