All research groups

Local and global invariants of dynamic systems, formal normal forms of dynamic systems and formal maps, local classifications of singularities, solvability of differential and functional equations on smooth manifolds, finite dimensional linear analysis, infinite dimensional nonlinear analysis.

Differential Equations, differential-functional and difference equations

Partial and ordinary differential Equations, intergral differential equations, stability of oscillatory systems, control systems

Functional-Differential and hybrid systems, control and optimization problems, neural networks, operator theory

Functional analysis: Sobolev spaces, global analysis: analysis on manifolds and L2-cohomology, geometrical theory of functions: quasi-conformal mappings, chemical engineering science.

Free boundary and variational problems, numerical methods, mathematical modeling, granular mechanics, applied super- conductivity

Unsteady-state problems of mathematical physics, mathematical modelling of wave and fracture propagation in solids and structures, dynamic strength and stability of composites under impact. Mathematical models of penetration processes and protective structure optimal design.

Partial differential equations, geometric measure theory

Dualitative properties of partial differential equations. mathematical models of water disalination by electro-dialysis

Theory of nonlinear transport processes in continuous media, specific interests: mass and momentum transfer in electrolyte solutions, synthetic ion-exchange membranes, reaction-diffusion, free boundary problems in heat and mass transfer.

Functional differential equations and their applications in spectral theory of Schroedinger operator, dynamical systems and probability theory.

Differential equations, asymptotic theory of differential operators

Enumerative combinatorics with applications in number theory, applied coding theory

Combinatorial geometry, topological graph theory, convex polytopes

Finite permutation groups, algebraic combinatorics, graph theory, mathematical chemistry

Applied Probability, Combinatorial Optimization, Number Theory.

Set theory, mathematical logic, combinatorics.

Computational and combinatorial geometry, sensor and wireless networks, online algorithms, discrete math.

Finite group theory, finite geometries, combinatorial topology.

Geometric Group theory, Expander graphs and High Dimensional Expanders, Coarse geometry

Discrete Geometry, Combinatorics, Dynamical Systems, Ergodic Theory, Diophantine Approximations, Computational Geometry

Representation Theory: Lie algebras and superalgebras, representations of finite groups, tensor categories, representation stability, diagram categories, categorical actions

Applied Probability, Combinatorial Optimization, Number Theory.

Geometric groups theory, Locally compact groups and their lattices, Invariant random subgroups, Permutation groups, Expanding graphs.

Ergodic theory and dynamical systems,  in particular symbolic dynamics and related aspects of probability theory. 

Geometric Group theory, Expander graphs and High Dimensional Expanders, Coarse geometry

Discrete Geometry, Combinatorics, Dynamical Systems, Ergodic Theory, Diophantine Approximations, Computational Geometry

Ergodic Theory, Random walks on groups, Geometric Group Theory.

Systems and control theory, operator theory in Hilbert spaces, module theory and linear algebra

Operator theory, linear systems, optimal control

Operator algebras

Topological groups (general theory), abstract harmonic analysis, topological dynamics

Operator theory, functional analysis, matrix theory.

Complex analysis, spectral theory of differential operators, functional equations.

Partial differential equations, geometric measure theory

Operator theory, system theory, algebraic geometry

Geometric analysis: Sobolev spaces theory. Quasiconformal analysis. Geometric measure theory. Analysis on metric measure spaces.

Operator algebras.

Knot Theory: Vassiliev invariants, Heegaard Floer and Khovanov homologies.

Symplectic geometry and low-dimensional topology.

Braid groups, mapping class groups and transformation groups of smooth manifolds: quasi- morphisms, norms.

Geometric group theory: quasi-isometric embeddings of finitely generated groups, bi-invariant word metrics.

Topology, dimension theory, geometric topology, continuum theory

Set theory, mathematical logic, concurrency (in Computer Science)

Semigroup theory, semigroup identities, completely o-simple semigroups, transformation semigroups, universal algebra

Theory of Lie algebras, constructive algebraic geometry, algorithmic problems in the theory of rings.

Set theory, mathematical logic, combinatorics.

Model theory and applications to algebra and geometry.

Set theoretic topology, functional analysis, topological groups.

Model theory (a branch of mathematical logic), and its interactions with other areas of mathematics, especially algebraic geometry, representation theory and differential equations. I also like algebraic geometry in general, as well as category theory and related subjects.

Stochastic processes, characterization problems of statistics, theory of function spaces.

Ergodic theory and dynamical systems, operator algebra, random processes.

Probability and statistics

Probability: random walks, interacting particle systems, discrete analysis. Geometric group theory: spaces of harmonic functions on groups, random walks on groups, boundaries.

Applied Probability, Combinatorial Optimization, Number Theory.

Ergodic theory, Markov operators