SPP 2265:  Random geometric systems

• Subject Area: Mathematics ; Computer Science, Systems and Electrical Engineering ; Physics ; Thermal Engineering/Process Engineering
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 422743078

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 will be dominant, but simulations, numerical, statistical and modelling work will also be part of the programme. Many questions of intrinsic mathematical interest will be attacked. Disciplines like physics, materials science and telecommunication will be crucial sources of problems, 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. The coordination fonds will be used to facilitate a broad and efficient exchange and activities program for the participants of the PP and further researchers working at research units in Germany and around.

• DFG Programme: Priority Programmes
• International Connection: Czech Republic, Hungary, Italy, Switzerland, United Kingdom

Projects

• Algebraic and Metric Properties of Random Geometric Graphs and Complexes (Applicants Reitzner, Matthias ;  Römer, Tim )
• Biased Random Walks and Exclusion Processes on Random Graphs (Applicants Gantert, Nina Jael ;  Klenke, Achim )
• Concentration and Cumulants for Stabilizing Functionals on Point Processes (Applicant Thäle, Christoph )
• Condensation in random geometric graphs (Applicant Mörters, Peter )
• Coordination Funds (Applicant König, Wolfgang )
• Critical behaviour of the weight-dependent random connection model (Applicant Heydenreich, Markus )
• Dynamics of Contact Processes on Simplicial Complexes (Applicants Gantert, Nina Jael ;  Kühn, Ph.D., Christian )
• Emergence of macroscopic phenomena in the non-linear hyperbolic supersymmetric sigma model - second phase (Applicants Disertori, Margherita ;  Merkl, Franz ;  Rolles, Silke )
• Gaussian Fluctuations in Models of Statistical Mechanics – Fine Asymptotics for the Magnetization (Applicants Döring, Hanna ;  Schubert, Kristina )
• Geometry of infinite clusters in continuum percolation models with strong correlations (Applicant Sapozhnikov, Artem )
• Gibbs point processes in random environment (Applicant Jahnel, Benedikt )
• Inhomogeneous spatial networks - beyond the weak decay regime (Applicant Mönch, Christian )
• Integral geometry in spaces of constant curvature and applications to stochastic geometry (Applicant Hug, Daniel )
• Limit theorems for stabilising functionals (Applicant Schulte, Matthias )
• Morphometric Roughness of Nanostructured Surfaces (Applicants Jacobs, Karin ;  Winter, Steffen )
• Optimal matching and balancing transport (Applicants Huesmann, Martin ;  Otto, Felix )
• Optimal transport for stationary point processes (Applicants Erbar, Matthias ;  Huesmann, Martin )
• Optimal transport for stationary point processes (Applicants Erbar, Matthias ;  Huesmann, Martin )
• Phase transitions in random loop models (Applicant Taggi, Ph.D., Lorenzo )
• Random polynomials and random Kähler geometry (Applicants Drewitz, Alexander ;  Marinescu, George Teodor )
• Random Polytopes (Applicant Kabluchko, Zakhar )
• Random polytopes (Applicant Kabluchko, Zakhar )
• Random Riemannian Geometry (Applicants Kopfer, Eva ;  Sturm, Karl-Theodor )
• Renormalization group for Gibbs point processes (Applicant Jansen, Sabine )
• Rigidity and hyperuniformity of point processes (Applicants Klatt, Michael Andreas ;  Last, Günter )
• Scaling limits of evolving spanning trees and of random walks on evolving spanning trees (Applicant Winter, Anita )
• Spatial Coagulation and Gelation (Applicants König, Wolfgang ;  Magnanini, Ph.D., Elena )
• Spatial growth and information exchange in evolving environments and on evolving networks (Applicants Hartung, Lisa ;  Klymovskiy, Anton )
• Spatial population models with local self-interactions (Applicants Birkner, Matthias ;  Gantert, Nina Jael )
• Spread of an infection in a time evolving structured population (Applicant Seiler, Marco )
• Stochastic geometry in non-Euclidean spaces (Applicants Gusakova, Anna ;  Thäle, Christoph )
• Superconcentration in random geometric structures (Applicant Bhattacharjee, Ph.D., Chinmoy )
• The Heat Flow of Random Polynomials (Applicant Jalowy, Jonas )
• The statistical mechanics of the interlacement point process (Applicants Drewitz, Alexander ;  Jahnel, Benedikt ;  König, Wolfgang )
• Towards Rigorous Results for Glassy Dynamics (Applicant Sperl, Matthias )
• Uniqueness theorems and analysis of classical density functional theory in nonequilibrium random geometries (Applicants Löwen, Hartmut ;  Wittmann, René )

• Spokesperson: Professor Dr. Wolfgang König