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Scientific research
Research Areas
Theoretical mathematics
- Geometry and topology
- Differential equations and mathematical physics
- Theory of functions, real, complex and functional analysis
- Algebra and number theory
- Discrete mathematics, computational mathematics, artificial intelligence
- Theory of probability and mathematical statistics
- Mathematical problems of mechanics
- Asymptotic and variational methods of complex analysis in dynamical systems and partial differential equations
- Classical and quantum kinetic equations
- Construction, analysis and testing of randomized and deterministic control systems
Mathematical modeling
- Mathematical modeling in problems of physics and chemistry
- Mathematical modeling of socio-economic processes
- Mathematical modeling in biology and medicine
- Mathematical modeling of multiscale interaction of the atmosphere and land for the tasks of weather forecasting, climate theory and environmental protection
- The method of boundary integral equations in the problems of radiation and reception of electromagnetic waves
- Modeling complex natural systems using lattice models for representing geometric-topological structure objects
- Development of modeling methods for pressing problems of gas dynamics, hydrodynamics, aerodynamics, turbulent flows
- Mathematical modeling in problems of magnetic hydrodynamics
- Supercomputer modeling of properties and virtual design of environment and materials with resolution of their microstructure
- Mathematical modeling in immunology
- Creation of technologies for modeling the dynamics of the ocean and sea ice, based on the use of finite-volume and finite-element methods and unstructured triangular-rectangular grids on the sphere
- Creation of a software package for the analysis of chaotic dynamic systems generated by atmospheric and ocean dynamics models
- Development of mathematical models, algorithms and software for digital nutrition
- Massively parallel economical algorithms in atmospheric dynamics models
- Computational methods and algorithms for numerical modeling of turbulence in the atmospheric boundary layer
Computational mathematics
- Development and research of numerical methods
- Development of tensor methods for approximating multidimensional arrays, the method of integral equations and their application
- Development of visual analytical methods for analyzing large volumes of data using computational tools
mathematics, high performance computing and interactive visualization - Algorithms for calculations in modern high-energy physics
- Development of applied methods of multi-agent predictive modeling of social resonance for significant events
based on analysis of large text collections - Development of high precision methods for solving equations of mathematical physics
- Development of new methods for solving grid equations
- Development of linear algebra methods in nonlinear approximation problems and optimization algorithms
- Development of discretization methods for equations describing filtration processes in fractured heterogeneous reservoir environments
- Development and research of algorithms for solving variational data assimilation problems in mathematical physics problems
- Optimization of computational algorithms for stability analysis of physical, technical and biological systems
- The effective theory of Riemann surfaces and their families
Theoretical computer science
- Data analysis
- Mathematical methods for decision support, artificial intelligence, neural networks and control systems
- Processing and analysis of images and signals
High performance computing
- Development of high-performance simulation and design methods for tomographs in wave models on a supercomputer
- High-performance algorithms for solving direct and inverse problems in the optics of layered media
- The use of supercomputers for medical purposes
- Development and application of probabilistic predictive models based on Bayesian networks using high-performance computing for personalized medicine
- Atomistic modeling of spraying processes of multilayer optical coatings using molecular dynamics, quantum chemistry and high-performance computing
- Mathematical models of large supercomputer centers
- Parallel algorithm structure
- Methods for supercomputer code design for solving graph problems
- Models, methods and tools for ensuring the quality of work of supercomputer centers
- Development of new parallel algorithms and software systems for computing systems with extra-massive parallelism
- Development of high-level languages, parallelization automation tools and software infrastructure for high-performance computing