Luisa Andreis, Franziska Flegel, Alexander Hinsen, Benedikt Jahnel, Robert I. A. Patterson, D. R. Michiel Renger, Lorenzo Taggi, Willem van Zuijlen
Christina van de Sand
from left to right: Wolfgang König, Alexander Wapenhans, Willem van Zuijlen, Christina van de Sand, Renato Soares dos Santos, Michiel Renger, Franziska Flegel, Robert Patterson, Benedikt Jahnel (small picture: Luisa Andreis, missing: Wolfgang Wagner)
OverviewThe research group mathematically analyses interacting random systems with a large number of degrees of freedom. Examples come from statistical physics, telecommunication, flow theory, population genetics, and matterials science. The interactions are usually defined on a microscopic scale, and the macroscopic (sometimes also the mesoscopic) behaviour is described with the help of methods from asymptotic probability theory (ergodic theorems, large deviations, martingale theory, weak convergence of measures, ...), but also from analysis (variational analysis, spectral theory, partial differential equations, ...).
Topics (selection)Some of the main subjects of the group concern questions about the stress field of localised versus homogenised behaviour of eigenfunctions of random operators, the use of stochastic particle systems as efficient solvers of kinetic equations, questions about connectivity, interference and capacity in spatial models for wireless communication, long-time behaviour of branching processes on gene sequences in random media and condensation and crystallisation phenomena in many-body systems at low temperatures. In the core topics of the group, the DFG decided in March 2019 to instal the Priority Programme SPP2265 "Random Geometric Systems" running 2020-26; the head of the Group is its coordinator.
Further activitiesThe group is also very active in the support of the exchange between mathematicians and the scientifically interested public, for instance by giving talks for school classes or for the public, or by editing books for the scientifically interested community. A particular highlight was the organisation of the 200th birthday of the Institute's eponym, Karl Weierstraß, another one the edition of the book ”Mathematics and Society”. Furthermore, the head of the group was in 2010-2019 the acting manager of the education centre in mathematics and the sciences INSPIRATA in Leipzig.
- Partial Differential Equations
- Laser Dynamics
- Numerical Mathematics and Scientific Computing
- Nonlinear Optimization and Inverse Problems
- Interacting Random Systems
- Stochastic Algorithms and Nonparametric Statistics
- Thermodynamic Modeling and Analysis of Phase Transitions
- Nonsmooth Variational Problems and Operator Equations