Fabian Haiden, IMADA, is new Sapere Aude Research leader

Today, Independent Research Fund Denmark has awarded its 2023 Sapere Aude Research Leader grants to talented, younger researchers who are ready to lead a research project at a high international level. The grant allows the researchers to develop and strengthen their research ideas and start their own research groups.

At SDU, seven researchers have received a Sapere Aude Research Leader grant, and one of them is Fabian Haiden, assistant professor at Department of Mathematics and Computer Science. He is also affiliated with Centre for Quantum Mathematics, and the research group Topology, Algebra, Analysis and Geometry.

With the grant follows DKK 6.192.000. The project title is: Topology, Algebra, Analysis and Geometry.

Project description

It is a remarkable idea, going back to Descartes, that there is a duality between geometry - the study of shape and space - and algebra - the study of formal operations. On a practical level, this means that problems in one subject can be translated into the other, where they might be easier to solve.

For modern applications in high-energy physics, computer science, and other subjects, a powerful algebraic language - category theory - has emerged. A category is an abstract mathematical structure with nodes, arrows between them, and a way of composing (multiplying) arrows.

The question this project seeks to answer: What is the geometry described by a category? If you could take a picture of a category, what would it look like? This problem lies at the heart of difficult and fundamental questions in geometry and mathematical physics, such as the origins of space itself.

Our approach is based on stability, which asserts that the points of the hypothetical space are in one-to-one correspondence with a certain subset of the nodes of the category, the "stable" ones. The mathematical problem is to select a consistent set of such stable nodes.

Together with a team working at SDU's recently established Centre for Quantum Mathematics (QM) and embedded in an international network of world-leading experts on the subject, Fabian Haiden will achieve new breakthroughs on this problem.