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

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.

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.

Differential Equations, differential-functional and difference equations

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

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

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

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

Partial differential equations, geometric measure theory

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

Differential equations, asymptotic theory of differential operators

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.

Enumerative combinatorics with applications in number theory, applied coding theory

Combinatorial geometry, topological graph theory, convex polytopes

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

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

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

Set theory, mathematical logic, combinatorics.

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

Finite group theory, finite geometries, combinatorial topology.

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

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. 

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

Operator theory, functional analysis, matrix theory.

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

Dynamical Systems and Ergodic Theory

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

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

• Quaternionic analysis. Function theory on Riemann surfaces. Linear system theory
• Infinite dimensional analysis, Hida’s white noise space, Gaussian processes

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

Operator algebras.

Operator theory, system theory, algebraic geometry

Operator algebras

Partial differential equations, geometric measure theory

Operator theory, linear systems, optimal control

Dynamical Systems and Ergodic Theory

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)

Model theory and applications to algebra and geometry.

Set theoretic topology, functional analysis, topological groups.

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

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

Set theory, mathematical logic, combinatorics.

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.

Dynamical Systems and Ergodic Theory

Ergodic theory, Markov operators

Probability and statistics

• Quaternionic analysis. Function theory on Riemann surfaces. Linear system theory
• Infinite dimensional analysis, Hida’s white noise space, Gaussian processes

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

Applied Probability, Combinatorial Optimization, Number Theory.

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

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