St. Petersburg Seminar
on Representation Theory and Dynamical Systems
Wednesday, 17 PM, room 311 , PDMI, Fontanka
Former talks in 2001:
T.Nagnibeda (KTH Stockholm)
Ergodic properties of boundary actions.
Classification of measurable functions in several variables and
random equidistributed matrices.
Anosov diffeomorphisms on the quotients of nilpotent
groups by discrete subgroups.
Methods of noncommutative computer algebra.
Quantum groups, Barnes functions, q-deformation Toda chains,
and modular duality.
Branching groups and their applications.
Christian Mauduit (Marseille)
Pseudorandom finite sequences
ASM matrices and calculation of the statistical sum for the 6-vertex model
Characters and representations of the Heisenberg group over the
algebraic closure of a finite field
Vadim Kaimanovich (Rennes)
Measures on laminations related to rational mappings
Xavier Bressaud (Marseille)
Knitting theory (or coding the action of braid groups on simple loops of
Youth Day: P.Nikitin, A. & M. Gorbulsky, S.Dobrynin, K.Kohas, V.Kunitsyn
Impressions of some conferences in USA
Unique $\beta$-expansions, one-dimensional
"mappings with holes", and digital channels
April 16, 25
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.
Asymptotical lower bound for the dimension of the space of Vassiliev-Goussarov
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.
S.V.Chmutov, S.V.Duzhin. A lower bound for the number
of Vassiliev knot invariants. "Topology and its Applications" 92 (1999)
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.
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.
About workshops in Marseille and Vienne
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.
Spherical designs and reflection groops
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