This purely mathematical project is driven by motivation and needs coming from Mathematical Physics. Cartan geometry and the related tractor calculi belong to fundamental approaches to geometric analysis with striking applications, based on structural understanding of the Lie theoretic algebraic tools. We shall develop essential extensions of such calculi to the realm of Lie super-groups and super-algebras, as well as to the higher geometry, topics very under-developed so far. Joining forces of top-level researchers in differential geometry, mathematical physics, and representation theory, we aim at creating new Cartan super-geometry and super-tractor calculus, and new Higher Cartan geometry. Blending the direct motivation coming from Physics with the strong background of the team in both Mathematics and Mathematical Physics will lead to new concepts and tools in Mathematics, potentially relevant for innovative models in Physics.

Sustainable Development Goals

Masaryk University is committed to the UN Sustainable Development Goals, which aim to improve the conditions and quality of life on our planet by 2030.