Applications of parabolic geometries and BGG sequences
Applications of parabolic geometries and BGG sequences
Disciplines
Mathematics (100%)
Keywords
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Differential Geometry,
Geometric Structure,
Invariant Differential Operator,
Cartan geometry,
Geometric Compactification
The broader context of the topic is the field of differential geometry, which is a part of pure mathematics. The basic idea of differential geometry is to generalize geometric ideas and concepts to higher dimensions and large classes of spaces. These generalizations are based on general versions of differential calculus and integration, thus providing a connection to mathematical analysis. A fundamental example of the concepts studied in differential geometry is a broad variety of concepts of curvature. Since Einsteins theory of general relativity describes gravity via curvature of the geometry space -time, large parts of differential geometry have close connections to theoretical physics. Most of the geometric structures studied within the project bel ong to the class of so-called parabolic geometries. These belong to a part of differential geometry in which symmetries play a particularly important role, which provides a connection to other parts of pure mathematics, in particular the theory of Lie groups and Lie algebras. In addition to connections to general relativity, parabolic geometries also have connections to other parts of theoretical physics, in particular to quantum field theory. There is a large number of very efficient tools for the study of parabolic geometries available. Most of them have been developed in intense international research during the last two decades. The PI of the project was involved in several central parts of these developments. Some parts of the project aim at the further developments of these methods, but the main focus will be on new applications of the theory of parabolic geometries. These applications concern several areas of very active current research in mathematics (partly beyond differential geometry) and theoretical physics.
- Universität Wien - 100%
- Boris Doubrov, Belarus State University Minsk - Belarus
- Vladimir Soucek, Charles University Prague - Czechia
- Pierre Julg, Université d´Orléans - France
- Thomas Mettler, Johann Wolfgang Goethe Universität Frankfurt am Main - Germany
- Rod A. Gover, University of Auckland - New Zealand
- Dennis The, University of Tromso - Norway
Research Output
- 15 Citations
- 5 Publications
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2022
Title BGG sequences with weak regularity and applications DOI 10.48550/arxiv.2203.01300 Type Preprint Author Cap A -
2022
Title Bundles of Weyl structures and invariant calculus for parabolic geometries DOI 10.48550/arxiv.2210.16652 Type Preprint Author Cap A -
2022
Title Geometric theory of Weyl structures DOI 10.1142/s0219199722500262 Type Journal Article Author Cap A Journal Communications in Contemporary Mathematics Pages 2250026 Link Publication -
2023
Title Bundles of Weyl structures and invariant calculus for parabolic geometries DOI 10.1090/conm/788/15819 Type Book Chapter Author Cap A Publisher American Mathematical Society (AMS) Pages 53-72 Link Publication -
2023
Title BGG Sequences with Weak Regularity and Applications DOI 10.1007/s10208-023-09608-9 Type Journal Article Author Cap A Journal Foundations of Computational Mathematics Pages 1145-1184 Link Publication