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Project information
Cartan supergeometries and Higher Cartan geometries

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Project Identification
GA24-10887S
Project Period
1/2024 - 12/2026
Investor / Pogramme / Project type
Czech Science Foundation
  • Standard Projects
MU Faculty or unit
Faculty of Science
Keywords
Cartan geometry; tractor calculus; super geometry; higher geometry; Lie super-group; Lie superalgebra; higher connection
Cooperating Organization
Charles University
  • Responsible person prof. Ing. Branislav Jurčo, CSc., DSc.

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.

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Publications

Total number of publications: 10

2025

2024

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