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.

Algorithmic problems in algebras. Semigroups theory. Groups theory.

Branching processes, random walks.

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.

Function approximations. Extremum problems. Trigonometric polynomials as well as the other orthogonal polynomial systems. Cubature formulae. Discrete geometry.

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

Experiments in discrete mathematics.

Mathematical logic. Proof theory. Provability logic. Modal logic. Fragments of arithmetic.

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

Functional spaces. Imbeddings. Approximation of classes of functions.

Trigonometric and orthogonal series. Functional spaces. Bases and almost everywhere convergence.

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.

Discrete probability theory, branching processes, statistical analysis of discrete sequences.

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 $n$ dimensions. Quasicrystals. Aperiodic tilings. Rigid and flexible polyhedra. Ising model. Mathematical education.

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

Low-dimensional topology.

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.

Variation calculus. Theory of optimal control. Differential-geometrical methods in the theory of extreme problems. Chronological calculus. Differential games.

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

Ergodic theory of noncommutative groups of transformations.

Birational geometry. Rationality problem. Birational rigidity. Degenerations of algebraic varieties. Monodromy.

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.

Geometry. Topology. Singularity theory. Characteristic classes.

Ergodic theorems for group actions, Markov partitions.

Combinatorial and probabilistic problems.

Multiple Fourier series. Absolute convergence. Lie group analysis. Ordinary differential equations. Symmetries.

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.

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.

Combinatorial and probabilistic problems and statistical applications.

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

Algebraic geometry and topology of algebraical manifolds.

Magnetohydrodynamics. Shock waves in continuous media. Asymptotical methods for stability of flows of continuous media in extended regions.

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

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.

Combinatorial group theory. Algorithmic problems of group theory.

Combinatorial group theory. Algorithmic problems of semigropus theory.

General algebraic topology. Topological semigroups of maps. Iterative Post algebras.

Number theory. Algebraic geometry. Algebra. Codes. Complexity. Differential equations. Mathematical physics.

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.

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

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

Combinatorial and probabilistic problems, random allocations of particles, sums of dependent indicators.

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

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.

Geometry. Topology. Homotopy. Classification of manifolds. Bordisms. Foliations. Theoretical physics.

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.

Аlgebraic number theory and Galois theory. Algebraic geometry and n-dimensional local fields and their applications to arithmetics, geometry of manifolds, integrable systems, and quatum field theory. History of mathematics.

Dynamics of open quantum systems. Quantum control.

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.

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.

Mathematical physics. Statistical mechanics. Phase transitions. Measure. Functional integration. Dynamical systems.

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

Combinatorial and probabilistic problems and statistical applications.

Mathematical problems of computer science.

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.

Algebraic number theory. Algebraic geometry. Theory of Lie groups and Lie algebras. Commutative and associative algebras.

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.

Additive combinatorics, number theory, ergodic number theory.

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

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

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

Combinatorial group theory. Algorithmic problems for groups and semigroups.

Approximations of functions. Special trigonometric series. Extreme properties. Functions with bounded variation.Widths.

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.

Differential equations. Difference methods. Exponentially convergent block method for solving boundary problems for the Laplace equation on polygons and the conformal mapping of multiconnected polygons onto canonical domains.

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

Stochastic applications of Tauberian theorems.

Differential equations, theory of optimal control.

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.

Combinatorial and probabilistic problems, probability inequalities, branching processes, stochastic algorithms.