Russian
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Research areas of the Laboratory of Representation Theory and
Dynamical Systems

Representation theory.
 Asymptotic representation theory of classical groups.
 A new version of the representation theory of the symmetric
groups, Coxeter groups, local groups and algebras.
 Duality theory for AFalgebras.
 Algebraic and asymptotic combinatorics
with applications to statistical physics.
 Representations of infinitedimensional Lie groups, current
groups, KacMoody groups, big groups.

Dynamical systems
 Models of ergodic theory: symbolic dynamics, substitutional
and adic transformations, arithmetics and dynamical systems.
 The dynamical theory of polymorphisms and Markov operators.
 The theory of systems of sigmaalgebras
of measurable sets and their factorizations.
 Boundaries of random walks on graphs and groups.
 Measures of algebraic and combinatorial origin on infinitedimensional
spaces.

Combinatorial and algorithmic methods.
 The theory of associative schemes.
 Complexity in algebraic and combinatorial problems.
 Universality and randomness in geometrical and combinatorial
categories.
 Young diagrams, symmetric functions and their applications.
 Limit shapes of configurations and random diagrams.

Convex geometry and
combinatorial topology.
 Geometry of convex polytopes and configurations.
 Combinatorial methods in smooth topology.
 Combinatorial invariants in topology and differential geometry.

Matrix theory and numerical
linear algebra.
 Inequalities for eigenvalues and singular values of
matrices.
 Singularity/nonsingularity criteria for square matrices.
 The theory of nonnegative matrices.
 Preconditioning methods.
 Methods for solving linear algebraic equations.

Numerical methods for solving
multiparameter problems of algebra with
polynomial and rational occurrences of parameters.
 Spectral problems.
 Factorization of matrix and scalar polynomials.
 Solution of nonlinear systems of algebraic equations.

Computer algebra.
 Design and analysis of algorithms of computational
commutative and differential algebra.
 Applications of computer algebra to physics and
celestical mechanics.
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