Курс лекций профессора Марка Минеева (Лос-Аламос, США) "Integrable Laplacian Growth (Critical Account)"

Курс лекций по теме:
"Integrable Laplacian Growth (Critical Account)"

     1. Introduction:Experimental background in physics, geophysics, and biophysics.
         Classical background in the Inverse Potential Problem and the dynamical systems with a "pole decomposition".

     2. Pattern selection far from equilibrium:The Saffman-Taylor finger, failed          

         attempts to include surface tension into the theory. The infinite list of the                    

         conservation laws. Exact singular solutions (which blow up in a finite time).

      3. Non-singular exact solutions and the selection without 

          surface tension: genus zero, genus one, and arbitrary genus (multi-bubble 

          dynamics).

      4. Integrable structure of Laplacian growth: quantum gravity, two-

          dimensional Toda hierarchy, and LG in terms of normal random matrices. 

          Relations to existing integrable systems of the hydrodynamic type.

       5. Universal fractal  growth of diffusion-limited aggregation. Stochastic 

           Laplacian growth. Tau-function and the statistical mechanics of unstable 

           growth.

       6. If time permits, I'll also deliver a sixth lecture on integrable structure of 

            other unstable processes, such as a Stokes growth and a 

            Loewner dynamics.