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Research Centre for Mathematical Modelling (RCM²)

Campus der Universität Bielefeld — © Universität Bielefeld

RCM²- research foci

RCM² is an inter-departmental institution of Bielefeld University that provides a common platform for applications of mathematics to the sciences. The activities include both research and training in mathematical modelling and in mathematical solution techniques.

Within the centre as well as with national and international partners, a large number of interdisciplinary cooperations have been established that have led to joint publications, organisation of workshops across disciplines, and to jointly guided PhD projects.

The current main focus of the centre is on research projects in:

mathematical biology, where RCM² members investigate questions of ecology, evolution, and neurobiology with the help of discrete and continuous dynamical systems, stochastic processes, and deterministic and stochastic simulation models. Beside their benefits for applications, the stochastic processes studied here lead to the exploration of new mathematical structures and hence give new impulses to probability theory as well.
mathematical data science, where RCM² members develop and employ mathematical models and new algorithmic and statistical methods for bioinformatics, cheminformatics, and ecology. This ties in with the increasing activity at the Faculty of Mathematics to analyse such methods with tools from statistics, high-dimensional probability, stochastic PDEs, random matrix theory, and (differential) geometry.
mathematical physics, where RCM² members are concerned with the spectral theory of nonperiodic structures, dynamical systems, random matrix theory, and spin systems. The former seeks a concrete structure classification via spectral types and topological invariants. Random matrices with their universal structures provide a versatile basis for the understanding of qualitative and quantitative features in a whole range of applications in physics, statistics, and economics. Spin systems are dealt with for applications in quantum magnetism, and as a means to investigate fundamental questions of thermalisation and decoherence.