We are an interdisciplinary research team that on one hand carries out research in pure mathematics and on the other hand explores new approaches to complex systems in a wide range of domains, bringing in the spectrum of mathematical concepts and methods in novel ways.
- Translate the action functionals, the concepts and the computational tools of High Energy Theoretical Physics into mathematical structures.
This is both fertile and challenging because of the inherent symmetries and invariances.
- Clarify the fundamental biological concepts and develop the conceptual and mathematical tools for systems biology.
How can we integrate detailed studies of individual pathways, coarse-grained network analysis, and modern mathematical data analysis techniques?
- Develop an economic theory that does not depend on the notion of a fully rational representative agent and that does not reduce itself to equilibrium analysis, but that rather focusses on the dynamics of expectations of boundedly rational and heterogeneous individuals.
How is information generated and processed in human societies?
- Humans with their limited abilities are often more clever and innovative than theory allows them to be. In particular, they often find creative and unexpected, but efficient shortcuts for solving complicated problems.
How to formalize that and translate it into powerful structural heuristics in data analysis and machine learning?
- What is the right relation between theory and data driven approaches?
Can we transform mathematics from a tool of science, investigating particular structures emerging from other fields, into a science of tools, proposing which structures to look for and how to do that?
- What are the neuronal dynamics and the rules of thinking, and how are these embodied in the brain, that make the formation of complex concepts like coherent objects with interdependent features possible?
- What is common to the complex systems of biology, cognition and society, and what is specific to each of them? What are the appropriate concepts?
- Formalize and operationalize the concepts and notions of the humanities and social sciences and connect them with the tools of data analysis and machine learning.
To what extent can a global, data driven approach (distant reading) complement the traditional study of particular details (close reading)?
There exist many overlaps between these research topics, leading to much mutual stimulation. In particular, many group members participate in several topics.