Project information
Algebraic methods in geometry and topology
- Project Identification
- GA201/08/0397
- Project Period
- 1/2008 - 12/2012
- Investor / Pogramme / Project type
-
Czech Science Foundation
- Standard Projects
- MU Faculty or unit
- Faculty of Science
- Keywords
- differential operator, graph complex, Cartan connection, parabolic geometry
- Cooperating Organization
-
Institute of Mathematics of the ASCR, v. v. i.
- Responsible person RNDr. Martin Markl, DrSc.
- Responsible person prof. RNDr. Vladimír Souček, DrSc.
The aim of the project is to bring together mathematicians working in diverse but closely related fields (algebra, topology, differential geometry), emphasizing the synthesis that takes place in contemporary mathematics. More concretely, we mean the following topics.
(1) Applications of graph complexes to invariant differential operators, with particular attention paid to Riemann and symplectic geometry.
(2) Investigation of Cartan connections and parabolic geometries.
(3) Description of algebras of symmetries of differential operators and construction of operators of special types.
(4) Study of questions related to classification of hypersurfaces in CR-geometry.
(5) Construction of higher-dimensional analogs of the Dolbeaut complex as resolutions of the Dirac operator in several variables.
(6) Applications of homotopy methods to formal solutions of differential relations.
(7) Study of forms on low-dimensional manifolds and induced G-structures.
Publications
Total number of publications: 10
2017
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A Projective-to-Conformal Fefferman-Type Construction
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), year: 2017, volume: 13, edition: 81, DOI
2013
-
Normal Forms and Symmetries of Real Hypersurfaces of Finite Type in C-2
INDIANA UNIVERSITY MATHEMATICS JOURNAL, year: 2013, volume: 62, edition: 1
2012
-
Finite type hypersurfaces with divergent normal form
MATHEMATISCHE ANNALEN, year: 2012, volume: 354, edition: 3, DOI
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Free CR distributions
Central European Journal of Mathematics, year: 2012, volume: 10, edition: 5, DOI
2011
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Chern-Moser operators and weighted jet determination problems
Geometric Analysis of Several Complex Variables and Related Topics, year: 2011
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Infinitesimal CR automorphisms of hypersurfaces of finite type in ${\mathbb{C}}^2$
Archivum Mathematicum, year: 2011, volume: 47, edition: 5
2010
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Higher Order invariants of Levi Degenerate Hypersurfaces
Pure and Applied Mathematics Quarterly, year: 2010, volume: 6, edition: 4
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Inclusions between parabolic geometries
Pure and Applied Mathematics Quarterly, year: 2010, volume: 6, edition: 3
-
Local equivalence of symmetric hypersurfaces in C^2
Transactions of the American Mathematical Society, year: 2010, volume: 362, edition: 6
2009
-
Degenerate hypersurfaces with a two-parametric family of automorphisms
Complex Variables and Elliptic Equations, year: 2009, volume: 54, edition: 3-4