Research Topics

Foundations of Complex Systems

Understanding complex systems is an ambitious yet essential task, touching every facet of our world—from healthcare and climate change to the economy and human behavior. We develop new mathematics and statistics to better grasp the nature of these complex systems, ultimately enabling us to control and manage complexity.

Complex systems, by their nature, pose challenges to our understanding. They typically involve many components intricately connected through networks. Neither the parts nor the networks are static. Instead, they mutually influence each other as they co-evolve. This dynamic interplay represents fundamental problems in the scientific description of complex systems.

The bottlenecks for understanding complex systems in ways that would allow us to control and manage them are often of methodological nature. We do not have the necessary mathematical and computational methods and tools – yet. To make progress, it is imperative to develop mathematics and statistics tailored for networked dynamical systems, often distinct from traditional statistics and physics approaches. A fundamental challenge is how to deal with co-evolutionary systems in practical ways with new insights from mathematics, physics, and the statistics of correlated processes. We develop the necessary methodological approaches to address this challenge.

We aim to solve problems that have been hitherto impossible to treat in scientific terms. Our foundational research contributes to diverse research areas at the CSH and beyond. This encompasses specific challenges in mathematics, artificial intelligence, and statistics, as well as simulation techniques that aid in understanding collective phenomena, ranging from systemic risks in financial markets to the fragmentation of societies.


  • Understanding and controlling co-evolution dynamics of networked systems out-of-equilibrium.
  • Understanding systemic properties based on underlying network structures – emergence
  • Understanding dynamics of collective phenomena and their tipping points
  • Producing mathematical solutions for problems of other research groups
  • Supporting research across fields with simulation techniques for specific systems



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