Data and Mathematics, or Mathematics and Data

The webinar was jointly organised by IAS and Institute for Mathematical Sciences (IMS), NUS. This is the first public lecture of the IMS-IAS joint public lecture series on Mathematical Artificial Intelligence (AI). It is also affiliated with the IMS conference on "Applied Topology in Frontier Sciences", July 11-22, 2022.

Data-driven sciences are widely regarded as the fourth paradigm of sciences that will fundamentally change the society and our everyday lives. Recently, the remarkable achievement of AlphaFold2 for protein folding problem has ushered in a new era of AI for sciences. Advanced mathematical tools, from algebra, topology, geometry, combinatorics, etc, have demonstrated great power in data representation, characterisation, and modelling. The interdisciplinary research area of Mathematical AI has developed very fast and demonstrated great potential in data analysis.

The Ollivier-Ricci curvature for a network structure.

Prof Jürgen Jost, Director of Max Planck Institute for Mathematics in the Sciences, is a world-leading mathematician specialising in geometry and its applications in biology, complex systems, economics, and AI. His talk focused on the interplay between data and Mathematics, that is data in search of models and models looking for data. It covered a brief history of group theory for crystal data, differential equations for population evolution data, and geometry for graph data. In particular, Prof Jost discussed the recent progress on discrete Ricci and sectional curvature models and their applications in gene networks, brain networks, and neural networks from deep learning models. The geometric measurements can reveal intrinsic data structural properties that cannot be characterised by traditional approaches.

The webinar ended with an interactive Q&A session where Prof Jost addressed different questions related to AI models, brain data, and discrete geometry.

Assistant Professor Kelin XIA | SPMS NTU