Algebraic methods in geometry and topology
|Project Period:||1/2008 - 12/2012|
|Investor:||Czech Science Foundation|
|Programme / Project Type:||Standard Projects
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|Field:||BA - General mathematics (B - Physics and mathematics)|
|Keywords:||differential operator, graph complex, Cartan connection, parabolic geometry|
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.