Emeritus Group
Geometry and Complex Systems
The emeritus group of Jürgen Jost is 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.
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Research
Scientific Goals
- 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 focuses 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)?
News
Miscellaneous
16.05.24
Congratulations to Fabio Di Nocera
Fabio Di Nocera successfully defended his dissertation, in which he explores a formalism for creating a unified framework that allows the description of both, classical and quantum information geometry, together. Congratulations and our best wishes for the future.
In Conversation
15.12.23
Raffaella Mulas in Conversation With Jürgen Jost
Raffaella Mulas, former group leader at MPI MiS, interviewed Director Jürgen Jost. Explore Jost's journey in mathematics and beyond, and learn about the mysterious Erdős-Bacon number in their lighthearted conversation.
Research Briefs
28.09.23
What Lie Algebras Can Tell Us About Jordan Algebras
Our latest Research Brief from the group of Jürgen Jost explores links between algebra and geometry. They discuss connections between Jordan algebras and Lie groups and investigate symmetries in algebraic structures.
Press Releases
08.09.23
What Do Neurons, Fireflies and Dancing the Nutbush Have in Common?
Synchronicity is all around us, but it is poorly understood. Jürgen Jost, Joseph Lizier, and colleagues have now developed new tools to understand how human and natural networks fall in and out of sync.
Miscellaneous
02.08.23
Cohomological Field Theories Secure Successful Dissertation
Congratulations also go to Shuhan Jiang for his successful dissertation defense. He is a researcher in the group of Jürgen Jost, who was his advisor for his great work on "Mathematical Structures of Cohomological Field Theories". All the best for your future!
Math Planck People
10.07.23
Renata Possobon
Meet the latest addition to our Math Planck People roster: Renata Possobon. She is currently a PhD student in Jürgen Jost's Dynamical Systems Group and shares a closer glimpse into her academic pursuits in our portrait.
Research
03.05.23
Journey to the Final Structure: New Paper Reveals Six Stages of Periodic Table Development
Guillermo Restrepo and his colleagues describe the six steps the periodic table took to converge on its final structure. Their findings have just been published in the Nature journal Communications Chemistry.