Galois moduli of finite group schemes. $p$-Adic representations for the Galois group of local fields. The Iwasawa theory. Theory of $p$-extensions of local and global fields. Highest theory of branching.

Branching processes, random walks.

holographic correspondence, quantum field theory, quantum information theory, chaos theory, quantum complexity theory.

Variational calculus. Optimal control theory. Differential and geometric methods in theory of extremal problems. Chronological calculus.

General relativity and gravitation theory (mathematical methods). Theory of nonlinear integrable systems. Integrable reductions of Einstein's equations (internal structure, solution generating methods, and solution of nonlinear initial and boundary value problems). Investigation of nonlinear properties of gravitational fields and of their interactions with various matter fields via construction of physically interesting field configurations with subsequent analysis of their physical and geometrical properties.

Popularization of mathematics, mathematics education. Extremal problems of approximation theory.

Optimal control. Dynamic systems. Differential inclusions. Multivalued mappings. Nonsmooth analysis. Mathematical economics.

Analytic number theory, L-functions.

non-equilibrium dynamics of quantum systems

Nonlinear partial differential equations, optimal control, optimal economic growth problems.

Functional spaces. Imbeddings. Approximation of classes of functions.

Algebraic geometry. Complex, symplectic and Riemann geometry. Number theory. Topology.

Hamilton systems. Variational methods.

Noncommutative algebraic geometry. Algebraic Poisson brackets on projective manifolds. Theory of symplectic groupoids. Poisson Lie groups. Derived categories of coherent bundless on algebraic manifolds. Representations of associative algebras. Theory of t-structures in triangulated categories. Coherent algebras and their homological properties. Foundations of homological and homotopic algebras. Algebraic problems of filed theory. Classical Diophantine problems. Quantum invariants of topological manifolds.

Topology. Homotopy. Mathematical physics.

Ergodic theory.

Formal group laws.

Pade approximants. Continued fractions. Recurrent equations.

Analytic continuation. Removable singularities. Boundary properties. Complex-analytic sets. Almost-complex manifolds. Pseudoholomorphic curves. CR–theory. Plurisubharmonic functions. Approximation of functions in several complex variables.

Shock waves in media. Propagation of waves in elastic and viscoelastic media with dispersion. Nonuniqueness of solutions of automodel problems for nonlinear dynamical elasticity theory.

Branching processes, random environments, queues theory.

Lattices and tilings in multidimensional spaces. Crystalline and quasicrystalline structures. Aperiodic tilings. Theory of polytopes, rigid and flexible polyhedra. Geometric methods in Statistical Physics. Mathematical education, popularization of mathematics.

Generalized functions. Integral transforms in distributions spaces. Fourier analysis. Laplace transform. Operational calculi. Differentional equations.

Low-dimensional topology.

quantum integrable systems, algebraic Bethe ansatz, quantum dynamics, quantum many body scars, ultracold atoms, non-Hermitian Hamiltonians.

Computational methods of probability theory and mathematical statistics.

Analytic number theory. Automorphic functions. Kloosterman sums. $L$-functions. Continued fractions.

Algebraic and combinatorial topology, characteristic classes, triangulations of manifolds, realization of cycles, combinatorial geometry, convex polytopes, flexible polyhedra.

Algebraic geometry, arithmetic geometry, higher-dimensional adeles, K-theory, algebraic cycles.

Ergodic theory of noncommutative groups of transformations.

Boundary-value problems for differential equations

Noncommutative probabilty theory. Quantum information theory. Mathematical foundations of quantum theory. Communication and computing. Quantum and classical stochastic processes. Quantum Markov property and dynamical semigroups. Statistical structure of quantum theory. Quantum measurements.

Nonlinear waves. Dispersive and dissipative media. Hamiltonian systems. Orbital stability of bound states. Solitary waves. Exponential instability. Evans function. Collapse. Asymptotic methods. Qualitative theory of dynamical systems. Center manifold reduction. Normal forms.

Dynamical systems. Attractors. Bifurcation theory. Relaxation oscilations. Limit cycles. Abelian integrals.

Information systems in mathematics.

Ddifferential geometry. Gravity models. Geometric theory of defects.

quantum communication, quantum computing .

Ergodic theorems for group actions, Markov partitions.

Multiple Fourier series. Lie group analysis of differential equations. Popularization of mathematics, mathematics education.

Trigonometric series. Polynomials. Best approximation. Character sums.

Incomplete Kloosterman sums, argument of Riemann's zeta-function, power residues, the average number of power residues, the problem of Lehmer–Landau.

Measure theory, probability theory, infinite dimensional analysis.

Analytical mechanics with applications to adjacent areas of theory of dynamical systems. Variational calculus. Differential topology and stability theory.

Ultrametric and p-adic analysis and applications in physics and biology, quantum probability and applications in physics, stochastic limit of quantum theory.

Discrete functions theory, complexity problems.

quantum cryptography, quantum information theory.

Combinatorial and probabilistic problems and statistical applications.

Many-dimensional complex analysis. CR-manifolds. Holomorphic authomorphisms and mappings.

Algebraic geometry and topology of algebraical manifolds.

Categories of coherent sheaves on algebraic varieties. Derived and triangulated categories. Noncommutative algebraic geometry. Representation theory. Module varieties of coherent sheaves.

quantum control, nonlocality of quantum states.

Proof theory, substructural logics, Kleene star.

Optimal control and differential games. Nnonsmooth and nonlinear analysis. Differential inclusions and inequalities. Robust discontinuous feedback in stabilization of control systems. Optimal control and differential games.

Nonequilibrium statistical mechanics. Dynamical systems theory.

open quantum systems, classical and quantum kinetic equations.

quantum many-body dynamics, adiabatic approximation, adiabatic quantum computing, quantum integrable systems.

Combinatorial group theory. Algorithmic problems of group theory.

Relativistic equations of quandum physics. Dirac equation. Yang–Mills equation. Einstein equation. Clifford algebras and differential forms.

Flows of continuous media with chemical reactions and radiation transport. Movements of rigid and fluid particles and nonstationary gas flows. Propagation of more-than-one dimensional and nonstationary fronts of detonation. Initiation and extinction of detonation.

integrable systems, exactly solvable models

Geometric topology, combinatorial topology, algebraic topology of Polish spaces, homotopy type theory.

Group theory, topology, category theory, algebraic K-theory.

Algebraic and differential topology. Operator and C*-algebras. Index theory, K-theory. Dynamic systems. Mathematical modelling in ecology. Bioinformatics. Mathematical education.

optimal control, optimization methods, control of quantum systems.

Stochastic analysis. Optimal stopping problems. Fractional Brownian motion.

Many-dimensional complex analysis. Geometrical and topological methods of extension of analytical objects.

Qualitative problems of the theory of optimal control. The theory of differential games.

Algebraic Geometry. Integer-valued quadratic forms generated by reflections in hyperbolic spaces. Automorphic forms. Lorentzian Kac-Moody algebras.

Topology of plane real algebraical curves and surfaces. Braid theory.

Categories of coherent bundles on algebraic manifolds. Derived and triangulated categories. Noncommutative algebraic geometry. Reflection symmetries.

Algebraic geometry. Algebraical number theory. Integrable systems.

Optimal control for systems with distributed parameters. Inverse problems of dynamics. Differential games.

Proof theory, modal logic, decision problems.

Algebraic Topology, Topology of Manifolds, Combinatorial Geometry.

Popularization of mathematics, mathematics education. Pseudodifferential operators, super analysis.

Dynamics of open quantum systems. Quantum control.

control of open quantum systems

Computational complexity theory.

Algebraic transformation groups. Invariant theory. Algebraic groups and their representation theory. Homogeneous spaces. Lie groups and Lie algebras. Algebro-geometric aspects of algebraic transformation group theory. Affine algebraic geometry. Automorphism groups of algebraic varieties. Discrete reflection groups.

Algebraic geometry.

Higher-dimensional algebraic geometry. Geometric control theory.

non-equilibrium dynamics of quantum systems

Complex analysis. Theory of approximations of analytical functions. Padé approximations and their generalizations. Orthogonal polynomials. Potential theory. Equilibrium distribution.

Complexity of proofs and computations.

Analytic number theory.

Geometrical topology. General topology. Pattern recognition. Scheduling. Divergent series.

Combinatorial and probabilistic problems and statistical applications.

Pseudoconvex polyhedra. Invariant domains of holomorphy. Geometric quantization. Twistor quantization. Seiberg-Witten equations. Pseudoholomorphic curves. Vortex equations.

Boolean functions theory, combinatorial and probabilistic problems of discrete mathematics.

Proof theory. Nonclassical logics. Combinatory logic.

Infinite-dimensional Lie algebras related to Riemann surfaces, their representations, and related problems of mathematical physics.

Quantum information theory.

probability theory, mathematical statistics, stochastic processes, financial mathematics, and their applications.

Algebraic geometry, birational geometry, Fano varieties, Kahler–Einstein metrics.

Discrete geometry. Geometrical crystallography. Geometry of positive-definite quadratic forms.

probability logic, modal logic, computability theory.

Theory of rational approximations of analytic functions. Pade approximations. Inverse theorems. General orthogonal polynomials.

Combinatorial group theory. Algorithmic problems for groups and semigroups.

irreversible quantum dynamics with quadratic generators, exactly solvable models of non-Markov quantum dynamics, quantum theory of open systems.

Dynamical systems of classic mechanics.

Foundations of statistical mechanics and kinetics, Loschmidt's paradox, quantum dynamics in bounded domains, quantum cryptography.

Singularity theory. Topology. Complexity theory. Integral geometry. Symplectic geometry and topology. Partial differential equations. Complex analysis. Combinatorics.

Branching processes and applications in biology and queues theory, combinatorial and probabilistic problems.

quantum control, functional analysis.

Mathematical physics. p-Adic analysis. Including mathematical problems in quantum field theory. String theory. Gravity. Quantum information. Quantum optics.

Stochastic applications of Tauberian theorems.

Complex analysis. Hyperfunctions. Integral representations. Algebraic and geometric methods in partial differential equations. Mathematical methods in quantum theory.

Probability theory. Stochastic calculus. Stochastic control. Applications in financial mathematics.