Russian version

St. Petersburg Seminar

on Representation Theory and Dynamical Systems

Wednesday, 17 PM, room 311 , PDMI, Fontanka 27

Former talks in 2002:

December 18
Pairs of dynamical systems, and strange factor representations of type II1
Oktober 9
Harmonic analysis on totally disconnected groups, and uniform distributions
September 25
A.Turbiner (Mexico)
Exactly solvable models of integrable problems
September 25
G. van Dijk (Leiden)
On tensor products and Berezin kernels
September 18
Monomial orderings and universal Groebner bases
The Groebner bases introduced by Buchberger give us a canonical representation of ideals in the ring of polynomials. A Groebner basis is defined if an admissible monomial ordering is given. Nevertheless this monomial ordering used for the construction of Groebner base is not very important for many concrete problems solved by Groebner bases technique. We describe a construction of a universal base which uses only the natural partial ordering defined by usual monomial division. Also a topology on the set of all admissible monomial orderings will be defined. We prove that this set is equivalent to the Cantor set and deduce some algebraic consequences of this fact.

September 4
Statistics of Jordan forms and Young diagrams.
June 26
New applications of the universality theorems for spaces of representations of matroids by configurations of points of the projective space.
June 19
New and old problems on C*-algebras.
May 22 and 29, June 5
K_0 functor for C*-algebras. Algebra of rotations. AF-algebras.
April 24
B.Kruglikov (Tromso, Norway)
Integrable nonholonomic flows with positive topological entropy
We present a non-holonomic generalization of examples due to Bolsinov and Taimanov, where integrable Riemannian metrics with chaotic behaviour were constructued. We discuss properties of topological entropy in the non-compact case and also integrability of Carnot-Caratheodory metrics. The obtained metrics are the first examples of non-holonomic systems, which are smoothly integrable, but not integrable with polynomial by momenta integrals.

April 17
Random metric space is Uryson space
February 13 and 20
Schur processes, infinite wedge space, and random partitions
(a survey of papers by A.Okounkov)
January 16
D.V.Osin (Moscow)
Finitely generated groups with non-uniform properties
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