Luisa Andreis, Franziska Flegel, Adrián González Casanova Soberón, Benedikt Jahnel, Robert I. A. Patterson, D. R. Michiel Renger, Renato Soares dos Santos, Wolfgang Wagner, Alexander Wapenhans, Willem van Zuijlen
Christina van de Sand
from left to right Paul Keeler, Onur Gün, Benedikt Jahnel, Renato Soares dos Santos, Robert Patterson, Christian Hirsch (now LMU München), Michiel Renger, Franziska Flegel, Wolfgang König, Wolfgang Wagner, Chiranjib Mukherjee
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.
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 is 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