Research Groups

In 2021, the research is carried out in the framework of 13 projects specializing in various areas of modern mathematics.


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Spatial Dynamical Stochastic Processes 

Research Group Leaders: Sergey Foss, Professor, Evgenii Prokopenko, PhD                 

Research priorities: communication and queueing systems and networks, stochastic geometry, wired and wireless communication, stability, rare events, risk, light and heavy tails, compound renewal process, branching random walk, real data and probabilistic models, statistical tests, linear regression, weighted empirical regression process, statistical methods for diagnostics in medicine.           

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Inverse Problems in Natural Science 

Research Group Leader: Maksim Shishlenin, Professor                     

Research priorities: inverse and ill-posed problems, numerical methods, continuation problem, conditional stability, probabilistic representations, randomization, stochastic SVD algorithms and linear solvers, stochastic phase retrieving, x-ray diffraction, Bayesian inference, computational and applied geometry, computational and applied topology, evolution of porous materials, tomography, immunology, epidiomology.  



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Development of a program for optimizing the shape of the suction tubes of hydraulic turbines 

Research Group Leader: Vladimir Skorospelov, PhD

Research priorities: numerical modeling of fluid flow in a hydraulic turbine, multipurpose optimization of the shape of a suction pipe, algorithms for designing the shape of a suction pipe of a hydraulic turbine. 

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Logistics 

Research Group Leader: Yury Kochetov, Professor 

Research priorities: discrete placement problems, scheduling problems, optimization problems for automated systems, scheduling problems, multicriteria investment portfolio optimization problems.

           



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Applied digital technologies

Research Group Leader: Rustam Mullyadzhanov, Professor

Research priorities: machine learning, computational fluid dynamics, bubble recognition problem in multiphase flow, inverse scattering problem for nonlinear wave fields, focusing nonlinear Schrödinger equation.


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Digitalization of Mathematical Models and Intelligent Systems for Data Analysis

Research Group Leader: Nikolay Bazhenov, PhD

Research priorities: a new theory of on-line computation, classification problems in mathematics and theoretical computer science, a technical framework based on definability theory and priority construction.  


                          
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Axial algebras and related groups

Research Group Leader: Ilya Gorshkov, Professor

Research priorities: non-associative algebras, idempotents, the Griess algebra, Majorana algebras, axial algebras, Jordan algebras, Matsuo algebra, involutions, the Monster, finite simple groups, 3-transposition groups, 6-transposition groups.

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Applied Abstract Algebra: Algebraic Methods in Topology, Combinatorics and Computational Complexity

Research Group Leader: Andrey Vasil’ev, Professor

Research priorities: discrete algebraic structures and isomorphism problems, development of the theory of highly regular graphs, study of topological crystals and self-similar continua, knots equivalence and quandle isomorphism. 



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Cryptography and Information Security

Research Group Leader: Natalia Tokareva, PhD

Research priorities: resistance of modern ciphers to different types of cryptanalysis, cryptographic Boolean functions and APN functions, quantum computing and cryptography, SAT-solvers for cryptanalysis, codes and metrically regular sets, blockchain technologies. 

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Geometric Analysis and Applications

Research Group Leader: Maria Karmanova, Professor

Research priorities: complex problems of nonholonomic geometry and geometric control theory (studying geodesics of sub-Riemannian and sub-Finsler metrics, fine aspects of Rashevskii–Chow theorem, uniform domains, classes of surfaces in sub-Lorentzian geometry and the coarea formula), quasiconformal analysis (properties of various classes of mappings with bounded distortion, openness and discreteness of mappings), hypoelliptic operators theory (Hormander-type equations, sub-Riemannian heat kernels, heat equations on Banach spaces).      




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Geometric Aspects of Mathematical Physics

Research Group Leader: Andrey Mironov, Corresponding member of RAS, Professor

Research priorities: geodesic flows, integrable systems, Birkhoff billiard, Riemann surfaces with boundary, Gromov—Witten theory, Hurwitz numbers, partial differential equations, Hermitian 6-manifolds, Lagrangian submanifold, free boundary problem, well-posedness, plasma-vacuum interface, surface tension.



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Differential Equations and Dynamical Systems

Research Group Leader: Inessa Matveeva, PhD

Research priorities: direct and inverse problems for generalized hyperbolic equations of Sobolev type, quasi-hyperbolic and quasi-parabolic equations, equations of mixed type; stability theory of solutions to new classes of differential-difference equations; nonlinear problems in the theory of elasticity, deformable systems, and hydrodynamics.           




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Advanced mathematical models and numerical methods for Newtonian continuum mechanics with application to geophysics

Research Group Leader: Evgeniy Romenski, Professor

Research priorities: Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems, a unified hyperbolic model of continuum mechanics, computational fluid and solid mechanics, arbitrary high-order ADER-Discontinuous Galerkin schemes, discrete element method, Digital Rock Physics, diffuse interface, upscaling, geomechanics, multiscale and multi-physics processes. 



           




2019-2020 research projects.