"The aim of the project is to make a major step-change in developingnovel effective tools for studying complex systems based onstochastic geometry and stochastic evolution methods, on appropriatemethods of analysis and combinatorics, as well as on numericalmethods and computer simulations. The network we are going to createwill unite efforts of leading specialists in this area towardsscientific excellence, will establish new and strengthen existinglong-term collaboration links between them, and will train a newgeneration of young researchers in this multidisciplinary area.The proposed research is assumed to employ existing and to elaboratenew models of real-world object, and hence to have directapplications. The systems we are going to study consist of largenumber of interacting entities and may evolve in continuous spaceand time. Both their structure and evolution are of our interest.Such systems appear in broadly understood statistical physics,including its industrial applications, in spatial ecology,evolutionary and population biology, epidemiology, etc. In view ofthis, along with mathematicians the network includes physicists andbiologists working with the corresponding experimental data andexperienced in modeling real world objects of the mentioned areas.In this direction, we plan to study structure and properties ofcomplex networks, such as polymers, irregular and random graphs,random fields on graphs, and their applications in the mentionedareas. The microscopic evolution of complex systems of this typewill be studied in Markovian and time-delayed frameworks. Theirmeso- and macroscopic dynamics will be deduced from the microscopictheory by various types of scaling procedures. Along with systems ofinteracting entities we will study objects which can becharacterized as evolving complex shapes, where methods ofstochastic geometry ought to be especially effective. Such modelshave various applications, e.g., in neurogeometry and visua"