"Children's drawings" of A.Grothendieck and random arithmetic curves

KMS-states on infinite-dimensional groups

Statistics of random heaps and matchings

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)

A survey of A.Klyachko's paper on models

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.

Memorial session to commemorate the 60th birth anniversary of S.V.Kerov (1946-2000).

Representations of the Krichever-Novikov algebras

Application of continual integral to calculating the spectrum of the Laplacian on graphs.

The branching of the basic series of representations of the groups GL(n,q) under parabolic restriction

Structural geometrical properties of infinite-dimensional Lie groups in applications to equations of mathematical physics

Recursive models of partition structures

Discrete groups generated by complex reflections

The entropy of automorphisms of von Neumann algebras generated by II_1 factor representations of the groups S(\infty) and U(\infty)

Traces on the Brauer algebras and random walks on graded graphs

(a joint work with A.M.Vershik)

Dynamic Yang-Baxter equation and deformation quantization

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.

Unified theories for ergodic means and martingales

Universal metrics and isometry groups

1) Information on recent conferences.

2) Symmetries of tensors and grassmanization of Specht modules.

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