When it comes to the mathematical foundations underpinning modern AI systems, many conference rooms tend to fall quiet. At the Higher Order Opportunities and Challenges Workshop at RWTH Aachen, the opposite was the case.

Organised by the Computational Network Science group, the workshop brought together researchers working on higher-order structures in networks – hypergraphs, random walks on higher-order structures, synchronisation in dynamical systems. Topics that may appear abstract at first glance, but have direct implications for real-world applications.

Michael Banf used the opportunity to present our work at Perelyn on curvature-guided graph-to-hypergraph liftings. The approach demonstrates how Forman-Ricci curvature can be used to analyse the structure of a graph and systematically transform it into a more expressive hypergraph representation.

What we took away from this workshop goes beyond the talks themselves. It is the connections between disciplines – from pure mathematics to industrial application – that make events like this valuable. The ideas that emerge there often need time. But they set something in motion.

The full talk is available as a recording.

Here you can find the research paper.
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