St. Petersburg Seminar
on Representation Theory and Dynamical Systems
Wednesday, 17 PM, room 311 , PDMI, Fontanka
Former talks in 2002:
Pairs of dynamical systems, and strange factor representations
of type II1
Harmonic analysis on totally disconnected groups,
and uniform distributions
Exactly solvable models of integrable problems
G. van Dijk (Leiden)
On tensor products and Berezin kernels
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.
Statistics of Jordan forms and Young diagrams.
New applications of the universality theorems for spaces of
representations of matroids by configurations of points of
the projective space.
New and old problems on C*-algebras.
May 22 and 29, June 5
K_0 functor for C*-algebras. Algebra of rotations. AF-algebras.
B.Kruglikov (Tromso, Norway)
Integrable nonholonomic flows with positive
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
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)
Finitely generated groups with non-uniform properties
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