## on Representation Theory and Dynamical Systems

### Former talks in 2006:

December 20
P.Zograf
"Children's drawings" of A.Grothendieck and random arithmetic curves
November 8
N.I.Nessonov (Kharkov)
KMS-states on infinite-dimensional groups
October 25
S.Nechaev (FIAN, Moscow and Orsay, France)
Statistics of random heaps and matchings
October 18
E.Goryachko
The model of representations of the group GL(n,K), where K is a field of characteristics zero or a finite field (a survey of A.Klyachko's papers)
October 11
E.Goryachko
A survey of A.Klyachko's paper on models
October 4
G.Panina
Pseudotriangulations

We show that the following two (quite different!) problems have one and the same combinatorial background.

1. Carpenter's rule problem.
Can any carpenter's ruler (a closed planar non-crossing closed broken line) be straightened in the plane avoiding self-crossing?

2. A.D.Alexandrov's problem.
Given a smooth convex 3D-body K and a constant C which separates the principal curvature radii of K (i.e., R1 \leq C \leq R2 everywhere), is K necessarily a ball?

The talk is based on papers by R.Connelly, Y.Martinez-Maure, D.Orden, G.Rota, B.Servatius, H.Servatius, I.Streinu, W.Whiteley, the speaker, and others.

For details, see http://www.arxiv.org/abs/math.MG/0607171.

June 14
Memorial session to commemorate the 60th birth anniversary of S.V.Kerov (1946-2000).
May 17
O.Sheinman (Steklov Institute, Moscow)
Representations of the Krichever-Novikov algebras
May 10
P.N.Mnev
Application of continual integral to calculating the spectrum of the Laplacian on graphs.
May 10
E.E.Goryachko
The branching of the basic series of representations of the groups GL(n,q) under parabolic restriction
April 26
A.M.Lukatsky (Moscow)
Structural geometrical properties of infinite-dimensional Lie groups in applications to equations of mathematical physics
April 19
Yu.V.Yakubovich
Recursive models of partition structures
April 19
V.L.Popov (Steklov Institute, Moscow)
Discrete groups generated by complex reflections
April 12
M.S.Boyko (Kharkov)
The entropy of automorphisms of von Neumann algebras generated by II_1 factor representations of the groups S(\infty) and U(\infty)
April 5
P.Nikitin
Traces on the Brauer algebras and random walks on graded graphs
(a joint work with A.M.Vershik)
March 29
A.Mudrov
Dynamic Yang-Baxter equation and deformation quantization
March 22
Lev Birbrair (Universidade Federal do Cear'a, Brazil)
Focal decompositions of M.Peixoto and related problems in Geometry and Number Theory

Mauricio Peixoto intoduced the notion of Focal Decomposition as a Geometric Object related to investigation of ODE of the second order. We are going to intoduce a notion of Focal Equivalence of equations and to solve some classification problems related to this equivalence relation.

March 14
A.G.Kachurovskii (Novosibirsk)
Unified theories for ergodic means and martingales
March 13
A.M.Vershik
Universal metrics and isometry groups
February 15
A.M.Vershik
1) Information on recent conferences.
2) Symmetries of tensors and grassmanization of Specht modules.
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