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Societal challenges and scientific curiosity are important actuators for mathematics, and vice versa. This is especially true for differential geometry, a generic framework straddling many areas of science and technology, as it essentially deals with `stuff’ that furnishes space and time..

Our strategy is to engender and exploit synergies among said `X-geometries’ by investigating their common ground. This argues for an approach beyond axiomatics in terms of operational concepts (`algorithms’). Our stratagem is to pursue our mission by combining inductive and analytical reasoning, establishing differential geometry (i) as an overarching framework for distinct application areas to fruitfully exchange ideas, and (ii) as a firm basis for incorporating artificial intelligence techniques to learn from annotated data while respecting a priori geometric constraints (geometric deep learning).

We are currently working on the following programmes: neurogeometry, cardiovascular geometry and spacetime geometry.