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