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

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

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

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

Partial differential equations, geometric measure theory

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.

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

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

Besov spaces, sobolev spaces.

Combinatorial geometry, topological graph theory, convex polytopes

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

Set theory, mathematical logic, combinatorics.

Applied Probability, Combinatorial Optimization, Number Theory.

Finite group theory, finite geometries, combinatorial topology.

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

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

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

Algebraic Graph Theory, Group Theory, Permutation Groups

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. 

I work in the intersection between group dynamics and operator algebras. Most of my PhD work was devoted to understanding the structure of the crossed product structure.

Here are some(or all) of my publications:

1. Generalized Powers’ averaging for Commutative crossed products., to appear in Transactions of the American Mathematical Society, preprint available at arXiv:2101.02853 ; (Joint with Dan Ursu).

2. On Intermediate C-subalgebras of C-simple Group Actions, International Mathematics Research Notices, Volume 2021, Issue 21, November 2021, Pages 16191–16202, https://doi.org/10.1093/imrn/rnz291, preprint available at arXiv:1811.11381.

3. On simplicity of intermediate C*-algebras, Ergodic Theory and Dynamical Systems, 40(12), 3181-3187. doi:10.1017/etds.2019.34 ; (Joint with Mehrdad Kalantar)

Random walks on groups, Geometric Group Theory, Ergodic Theory and Operator Algebras

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

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

Ergodic theory, dynamical systems and related topics.

Operator theory, linear systems, optimal control

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

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

Operator theory, functional analysis, matrix theory.

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

Operator theory, system theory, algebraic geometry

Free Analysis, Operator Theory, Complex Analysis

operator algebras, noncommutative convexity, function theory, several complex variables, real and complex algebraic geometry

I work in the intersection between group dynamics and operator algebras. Most of my PhD work was devoted to understanding the structure of the crossed product structure.

Here are some(or all) of my publications:

1. Generalized Powers’ averaging for Commutative crossed products., to appear in Transactions of the American Mathematical Society, preprint available at arXiv:2101.02853 ; (Joint with Dan Ursu).

2. On Intermediate C-subalgebras of C-simple Group Actions, International Mathematics Research Notices, Volume 2021, Issue 21, November 2021, Pages 16191–16202, https://doi.org/10.1093/imrn/rnz291, preprint available at arXiv:1811.11381.

3. On simplicity of intermediate C*-algebras, Ergodic Theory and Dynamical Systems, 40(12), 3181-3187. doi:10.1017/etds.2019.34 ; (Joint with Mehrdad Kalantar)

Operator algebras.

Operator algebras

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

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

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

Partial differential equations, geometric measure theory

Besov spaces, sobolev spaces.

Set theoretic topology, functional analysis, topological groups.

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

Algebraic geometry, Tropical Geometry, Singularities

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

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.

Set theoretic topology, functional analysis, topological groups.

Model theory and applications to algebra and geometry.

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: 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