A survey of papers related to Kerov's central limit theorem for the Plancherel measure on Young diagrams

Refinement equations

Refinement equations are two-scale difference functional equations of the type

\phi(x)=\sum_{k=0}^N c where c_{k}\phi(2x-k),_{0},...,c_{N}are complex coefficients, N=1,2,... Such equations have been studied in great detail in connections with their role in the wavelets theory, subdivision schemes in the approximation theory and curve design, fractals, probability theory and so on. By the study of spectral properties of the corresponding linear operator Tf(x)=\sum_{k=0}^N c_{k}f(2x-k) (transition operator) we solve several problems in the theory of refinement equations. The properties of the solution \phi will also be discussed.

A new look at the Burnside-Schur theorem (a joint work with S.A.Evdokimov)

Noncommutative hypergeometry (a survey of A.Volkov's paper)

The limit form of Young diagrams for multiplicative statistics with intermediate growth

Constructing infinite words with intermediate subword complexity

Orbits and factor representations of arbitrary discrete nilpotent groups of class 2

Some applications of the Ramsey and dual Ramsey theorems in topological dynamics

Each topological group G admits a unique universal minimal dynamical system (M(G),G). For a locally compact non-compact group this is a nonmetrizable system with a rich structure, on which G acts effectively. However there are topological groups for which M(G) is the trivial one point system (groups with the fixed point on compacta property), as well as topological groups G for which M(G) is a metrizable space and for which one has an explicit description. I will survey this new theory as developed by Pestov, Uspenskij and Glasner and Weiss and show how it relies on combinatorial Ramsey type theorems.

Joint session of the seminar and the conference

Information on the conferences on group theory and others

Circles, quadratic mappings from spheres to spheres, and Clifford algebras

New counterexamples to an old uniqueness hypothesis for convex surfaces

We introduce a series of principally different C^\infty -smooth counterexamples to the hypothesis on characterization of the sphere:

If for a smooth convex body K in R^3 and a constant C, in each point of \partial K the principal curvature radii of \partial K are separated by C, then K is a ball.

The hypothesis was proved by A.D.Alexandrov and H.F.Muenzner for analitic bodies. For the general smooth case it remained an open problem for years. Recently, Y.Martinez-Maure presented a C^2-smooth counterexample to the hypothesis.

Optimal systems with restauration

Final blocking property for billiard systems

Schur rings over cyclic groups

On the "Random Growth" semester in Institut Henri Poincare and other news

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