SPP 2265: Random geometric systems

Basic data for this project

Description

This Priority Programme (PP) is devoted to the mathematical analysis of effects and phenomena that emerge from an interplay between randomness and geometry. Analytical work is dominant, but simulations, numerical, statistical and modelling work are also part of the programme. Many questions of intrinsic mathematical interest are attacked. Disciplines like physics, materials science and telecommunication are crucial sources of problems, motivations, models and solutions. The main focus lies on the development of new and the refinement of existing methods, and on the creation and analysis of new random spatial models. Goals comprise the rigorous description and analysis of emergence of macroscopic phenomena like condensation, percolation, crystallisation; geometric functionals of random structures like Minkowski functionals and cluster counts; new limiting geometries; geometric systems driven by correlated spatial randomness; metastability in spatial processes away from equilibrium; effects arising from kinetic or geometric constraints; new applied spatial random models.While these questions are fundamental and ubiquitous, the novelty of the proposed PP is a substantial further development into various timely directions, like time-dependent random media, continuous-space modelling, long-range dependence of interactions, description of entire geometries instead of characteristic quantities, the introduction of spatiality into mean-field models, and more. The most recent activities in the field are merged and further explored, new analytic and modelling paradigms are developed. A systematic transfer of questions from the applied sciences into mathematics is an integral part of this PP. In this sense, the proposed PP has an interdisciplinary outreach, with a major focus in probability.