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SUMMARY:New discretization of complex analysis and completely integrable s
 ystems - Novikov\, SP (Maryland)
DTSTART:20090327T153000Z
DTEND:20090327T163000Z
UID:TALK17562@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:New Discretization of Complex Analysis was developed recently 
 by the present author and I.Dynnikov. Our discretization has nothing to do
  with geometric discretization of conformal maps. We consider complex anal
 ysis as a theory of linear Cauchy-Riemann Operator. It is based on the Equ
 ilateral Triangle Lattice in the Euclidean Plane (the classical one was ba
 sed on the quadrilateral lattice). This approach allows us to borrow some 
 crucial ideas from the modern theory of Completely Integrable Systems miss
 ing in the case of quadrilateral lattice. New phenomena appear in the case
  of Equilateral Lattice in Hyperbolic (Lobachevski) Plane: geometric objec
 ts became ''stochastic'' requiring to use technic of Symbolic Dynamics. Ne
 w difficulties appear leading to the unsolved plroblems.
LOCATION:Seminar Room 1 Newton Institute
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