Доклады в 2010 году


23 June
A. A. Belavin (Inst. Teor. Fiz., Moskwa)
"TWO DIMENSIONAL GRAVITY IN MATRIX MODEL,
TOPOLOGICAL AND LIOUVILLE APPROACHES
"
Three different approaches to 2d Gravity will be discussed.
The first one is the continuous approach, in which the theory is defined
through the functional integral over the Riemannian metric with
appropriate gauge fixing. The choice of the conformal gauge leads
to quantum Liouville theory and for that reason this approach is
often called the Liouville Gravity.
The second one is the discrete approach, based
on the idea of approximating the fluctuating 2d geometry by an
ensemble of planar graphs, so that the continuous theory is
recovered in the scaling limit where the planar graphs of very
large size dominate. The discrete approach is usually refereed
to as the Matrix Models, since technically the ensemble of the graphs
is usually generated by the perturbative expansion of the integral
over $N\times N$ matrices.
The third approach is 2d topological gravity. Witten built axiomatics of
this theory by studying intersection theory on the moduli space of
Riemann surfaces.
It will be shown in what sense all these approaches are equivalent.



27 May
V.Tarasov (PDMI)
"Bethe subalgebras of the group algebra of the symmetric group
"
I will introduce a family of maximal commutative subalgebras, called Bethe
subalgebras, of the group algebra of the symmetric group. Bethe subalgebras
are deformations of the GelfandZetlin subalgebra. I will describe properties
of Bethe subalgebras.



1 April
E. K. Sklyanin (York, UK)
"Bispectrality and separation of variables
in multiparticle hypergeometric system
"
Hypergeometric functions depending on two sets
of parameters are known to possess the property
of bispectrality: they satisfy two different systems
of differential/difference equations in one set of
parameters the other plays the role of spectral parameter
and vice versa. Examples we choosen include the open
Toda lattice and Calogero  Sutherland system.



25 March
P. N. Mnev
"Towards (perturbative) topological quantum field theory
with boundary"
We will discuss the project of quantizing AKSZ
(AlexandrovKontsevichSchwarzZaboronsky) sigma models on manifolds
with boundary, in a way that is consistent with gluing. The motivation
here is drawn from the example of onedimensional ChernSimons theory
on an interval.



4 марта
Л.Д.Фаддеев
"3 + 1 separation of variables in new approach to the Einstein theory of gravity"

