The main and general objective of the project is to give a new impetus to the development of operator theory in Poland, the science having long but fading tradition in this country. We bridge the gaps in the Polish operator theory terrain by importing "new" areas and developing their links to fields already established in Poland. This will be achieved due to the high quality training by leading experts and intensive research collaboration with them. Our main focus is operator-theoretical approach to problems originating from differential equations. The transfer of knowledge will pursue the creation of a center of operator theory of European level in Warsaw. It will contribute towards integration of European scientific community.
Moreover, the expected scientific progress will secure the standard of European science in the field of operator theory and its applications in Poland on the international level, and the position of IM PAN as one of the most advanced mathematical centers in the central Europe.
The project is based on interaction of different areas of differential equations: semigroup theory, PDE's, numerical analysis, dynamical systems whose common denominator is operator theory.
Potential applications include mathematical biology: population dynamics (models of phytoplankton), genetics (e.g. size of paralogous gene families in genome), propagation of impulses in nerve fibers, physics (electromagnetic scattering, quantum and nonlinear optics, fluctuations of brightness of Milky-Way), chemistry (propagation of flame fronts in combustion problems), computer science (solving of a "large" linear algebra problems, stability and efficiency of computations), signal processing.