Phenomena that emerge from an interaction between random influences and geometric properties are ubiquitous and extremely diverse. They appear in physics (e.g., condensation or crystallisation in interacting random particle models for equilibrium situations), materials science (e.g., electrical conducting properties in metals with impurities), in telecommunication (e.g., connectivity in spatial multi-hop ad-hoc communication networks), and elsewhere. The origins and the mechanisms that lead to the phenomena are often deeply hidden. Bringing them to the surface often requires serious research activities, many of which have to be theoretical by the nature of the problem.
This Priority Programme is devoted to the mathematical analysis of effects and phenomena that emerge from an interplay between randomness and geometry. Many questions of intrinsic mathematical interest will be studied. Disciplines like physics, materials science and telecommunication will be crucial sources of problems, applications, motivations, models and solutions. The main focus will lie on the development of new and the refinement of existing methods, and on the creation and analysis of new random spatial models.
Proposals must be written in English and submitted to the DFG by 11 November 2019.