## on Representation Theory and Dynamical Systems

### Former talks in 2001:

December 19
T.Nagnibeda (KTH Stockholm)
Ergodic properties of boundary actions.
December 19
A.Vershik
Classification of measurable functions in several variables and random equidistributed matrices.
November 14
A.Suvorov
Anosov diffeomorphisms on the quotients of nilpotent groups by discrete subgroups.
October 24
V.Kornyak (Dubna)
Methods of noncommutative computer algebra.
October 10
M.A.Semenov-Tyan-Shanskii
Quantum groups, Barnes functions, q-deformation Toda chains, and modular duality.
October 3
R.I.Grigorchuk (Moscow)
Branching groups and their applications.
September 26
Christian Mauduit (Marseille)
Pseudorandom finite sequences
September 19
M.Zvonarev
ASM matrices and calculation of the statistical sum for the 6-vertex model
September 5
K.P.Kohas
Characters and representations of the Heisenberg group over the algebraic closure of a finite field
August 29
Measures on laminations related to rational mappings
August 22
Xavier Bressaud (Marseille)
Knitting theory (or coding the action of braid groups on simple loops of punctured disks)
June 6
Youth Day: P.Nikitin, A. & M. Gorbulsky, S.Dobrynin, K.Kohas, V.Kunitsyn
May 30
A.M.Vershik
Impressions of some conferences in USA
May 16
N.A.Sidorov
Unique $\beta$-expansions, one-dimensional "mappings with holes", and digital channels
April 16, 25
N.E.Mnev
Combinatorial models of classyfying spaces in piecewise-linear topology
A brief review of the theory of classifying spaces, the construction of the exact BPL model and the Gauss map for combinatorial manifolds.

April, 11
S.V.Duzhin
Asymptotical lower bound for the dimension of the space of Vassiliev-Goussarov invariants
The talk is about the lower bound for the number of independent knot invariants of finite type obtained in 1996 by S.Chmutov and S.Duzhin and improved in 1997 by O.Dasbach. Currently the best bound is exp(C \sqrt(n)) for any constant C < pi * \sqrt(2/3). The proofs consist in an explicit construction of a big family of independent elements in the space of uni-trivalent graphs, distinguished by a special linear mapping into the space of multivariate polynomials.

References:

S.V.Chmutov, S.V.Duzhin. A lower bound for the number of Vassiliev knot invariants. "Topology and its Applications" 92 (1999) 201-223.

O.Dasbach. On the Combinatorial Structure of Primitive Vassiliev Invariant III - A Lower Bound, Communications in Contemporary Mathematics, Vol. 2, No. 4, 2000, pp. 579-590.

March, 21
A.G.Ershler (Dyubina)
Estimation of some parameters for random walks on amenable groups
For symmetric random walks on finitely generated groups, examples of calculation of drift and entropy, and some inequalities relating these functions with the word function of growth of the group will be considered. Some new examples of zero and positive entropy will be given.

March, 14
A.M.Vershik
About workshops in Marseille and Vienne
January, 31
S.V.Duzhin
Combinatorial structures associated with finite type knot invariants
Due to the theorem of M.Kontsevich, the study of many properties of finite type knot invariants can be reduced to the study of graded algebras generated by combinatorial objects such as chord diagrams, Feynmann diagrams, 3-1-valent graphs etc. The talk will contain a survey of these algebras and an explanation of their relation to knot invariants. In particular, I will mention the upper and lower bounds for the number of independent finite type knot invariants obtained by combinatorial techniques.

January, 24
B.B.Venkov
Spherical designs and reflection groops

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