Sergei Novikov (Steklov Mathematical Institute and University of Maryland)
In our approach Complex Analysis is discretized as a theory of the linear Cauchy-Riemann operator (not the geometry of conformal mappings). Classical discretization of the Cauchy-Riemann operator is based on the square lattice (1940). Several ideas borrowed in the late 1990s from modern theory of completely integrable systems led to the conclusion that the Equilateral Triangle Lattice is much better for this goal than the Square Lattice. Last year the present author developed this approach (first work was done in collaboration with I. Dynnikov in 2002). In the most recent work some ideas borrowed from Symbolic Dynamics were also used. Mike Boyle from the University of Maryland helped here.