## on Representation Theory and Dynamical Systems

### Former talks in 2008:

December 30
Session in honor of A.M.Vershik's 75th anniversary
T.Nagnibeda. Dynamics of sand heaps on self-similar graphs.
A.Malyutin. Boundaries of the braid group.
A.Lodkin. Phyllotaxis and related problems.
M.Gordin. How one can see mixing.
Yu.Yakubovich. Ergodicity of some measures on partitions.
A.Gorbulsky. Vershik's scaling and secondary entropies: similarity and difference.
F.Petrov. On embeddings of metric spaces into normed spaces.
E.Goryachko. The K_0 functor and characters of the group of rational rearrangements of the segment.
December 17
Session dedicated to the memory of A.N.Livshits
1. A.M.Vershik. On the mathematical activity of A.N.Livshits.
2. A.M.Vershik. The number-theoretic version of the Morse transformation.
3. M.I.Gordin. Cohomology of dynamical systems: around Livshits' theory.
October 8
L.Petrov (Moscow)
Infinite-dimensional diffusions on the Kingman simplex
September 17
A.Sergeev
Deformed Calogero-Moser systems as restrictions of infinite-dimensional classical systems of the same type
August 21
Sergei Nechaev (LPTMS, Orsay and Lebedev Physical Institute, Moscow)
Geometry and statistics of growth models
July 2
B.Granovsky (Technion, Haifa)
Meinardus theorem on weighted partitions: Extensions and a probabilistic proof

The number $c_n$ of weighted partitions of an integer $n$ with parameters (weights) $b_k$, $k\geq 1$, is given by the generating function relationship $$\sum_{n=0}^{\infty}c_nz^n=\prod_{k=1}^\infty(1-z^k)^{-b_k}.$$ Meinardus (1954) established his famous asymptotic formula for $c_n$, as $n\to \infty$, under three conditions on power and Dirichlet generating functions for $b_k$. We give a probabilistic proof of Meinardus' theorem with weakened third condition and extend the resulting version of the theorem from weighted partitions to other two classic types of decomposable combinatorial structures, which are called assemblies and selections.

This is a joint work with Dudley Stark(Queen Mary College, London) and Michael Erlihson (Technion, Haifa).

June 18
A.M.Vershik
Invariant integration in spaces of discrete measures and convergent series
January 9
P.Mnev
Discretization of the algebra of differential forms on a manifold and topological quantum field theory
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