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.
Faculty of Mathematics and Physics CU
 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 CRgeometry.
(5) Construction of higherdimensional 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 lowdimensional manifolds and induced Gstructures.
Publications
Total number of publications: 10
2017

A ProjectivetoConformal FeffermanType 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 C2
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

Free CR distributions
Central European Journal of Mathematics, year: 2012, volume: 10, edition: 5, DOI
2011

ChernMoser operators and weighted jet determination problems
Geometric Analysis of Several Complex Variables and Related Topics, year: 2011

Infinitesimal CR automorphisms of hypersurfaces of finite type in ${\mathbb{C}}^2$
Archivum Mathematicum, year: 2011, volume: 47, edition: 5
2010

Higher Order invariants of Levi Degenerate Hypersurfaces
Pure and Applied Mathematics Quarterly, year: 2010, volume: 6, edition: 4

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 twoparametric family of automorphisms
Complex Variables and Elliptic Equations, year: 2009, volume: 54, edition: 34