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