Programme:
June 5^{th} 2006
Time 
Speaker/Event 
Title 
9:4510:45 
M. Blaszak 
Reciprocal transformations for
classical Stackel systems and related dispersionless systems 
10:4511:15 
Coffee 

11:1512:15 
A. Kokotov 
Determinants of Laplacians and
moduli spaces of Riemann surfaces and Abelian differentials. 
12:151:30 
Lunch 

1:302:30 
Y.Ohta 
T.B.A 
2:303:30 
S. Silvestrov 
QuasiLie algebras and twisted
derivations 
3:304:00 
Tea 

4:005:00 
S. Simirnov 
Discrete analogs of
VeselovShabat dressing chain 
Evening 
Dinner: Bar Milano, Byers
Road, 6:30pm 
Location:
Room 214, Department of Mathematics.
Titles and abstracts:
Reciprocal
transformations for classical Stackel systems and related dispersionless systems
Abstract:
Systematic construction of classical Stackel systems (these with all constants of motion quadratic in momenta) in
coordinate free way is presented. With each class of such systems one can relates weakly nonlinear
semihamiltonian dispersionless systems. It is shown that different classes of
Stackel systems as well as connected dispersionless systems are related by an
appropriate reciprocal transformations.
Determinants of Laplacians and moduli spaces of Riemann surfaces and Abelian
differentials.
Abstract:
The RaySinger formula for the determinant of the Laplacian on elliptic
surfaces is generalized to Laplacians in flat metrics with conical
singularities on compact Riemann surfaces of genus greater than 1. The result is given in terms of higher genus
generalization of Dedekind's etafunction.
One of potential applications of the determinant of Laplacian is,
according to the general approach of OsgoodPhilipsSarnak, to use it as a
Morse function on the space of metrics on Riemann surfaces of a given genus and
fixed area. We develop this idea for the case of genus two. By a
combination of analytical and numerical methods we find four stationary points
of the determinant of Laplacian on the moduli space; three of them correspond
to the surfaces with large groups of automorphisms. This allows to
calculate the orbifold Euler characteristics of the full moduli space of genus
two curves, reproducing the number
1/120 according to wellknown HarerZagier formula. For symmetric
strata of Riemann surfaces with D2, D3 and Z2 symmetry groups the
orbifold Euler characteristic are given by 1/2, 1/2
and 1/4 respectively.
S.Smirnov:
Discrete
analogs of VeselovShabat dressing chain
QuasiLie algebras and twisted derivations
Abstract:
In this talk the class of quasiLie algebras and some of its subclasses
will be presented. The
definitions will be explained, and examples coming from twisted derivations,
difference type
operators and other examples and constructions leading to quasiLie algebras
will be described.
Updated
2^{nd} June 2006