Research areas of the Laboratory of Representation Theory and
- 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 AF-algebras.
- Algebraic and asymptotic combinatorics
with applications to statistical physics.
- Representations of infinite-dimensional Lie groups, current
groups, Kac-Moody groups, big groups.
- 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 sigma-algebras
of measurable sets and their factorizations.
- Boundaries of random walks on graphs and groups.
- Measures of algebraic and combinatorial origin on infinite-dimensional
Combinatorial and algorithmic methods.
- The theory of associative schemes.
- Complexity in algebraic and combinatorial problems.
- Universality and randomness in geometrical and combinatorial
- Young diagrams, symmetric functions and their applications.
- Limit shapes of configurations and random diagrams.
Convex geometry and
- Geometry of convex polytopes and configurations.
- Combinatorial methods in smooth topology.
- Combinatorial invariants in topology and differential geometry.
Matrix theory and numerical
- Inequalities for eigenvalues and singular values of
- 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.
- Design and analysis of algorithms of computational
commutative and differential algebra.
- Applications of computer algebra to physics and
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