Project details

 

Algebraic methods in geometry and topology

Project Identification:GA201/08/0397
Project Period:1/2008 - 12/2012
Investor:link to a new windowCzech Science Foundation
Programme / Project Type:Standard Projects -
MU Faculty/Unit:
Faculty of Science
MU Investigator:Prof. RNDr. Jan Slovák, DrSc.
Project Team Member:Assoc. Prof. RNDr. Martin Kolář, Ph.D.
Bc. Lukáš Vokřínek, PhD.
Mgr. Vojtěch Žádník, Ph.D.
Cooperating Organization:
link to a new windowInstitute of Mathematics of the ASCR, v. v. i.
Responsible Person:RNDr. Martin Markl, DrSc.
link to a new windowFaculty of Mathematics and Physics CU Praha
Responsible Person:Prof. RNDr. Vladimír Souček, DrSc.
link to a new windowCharles University Prague
Field:BA - General mathematics (B - Physics and mathematics)
Publications/Results:more
Keywords:differential operator, graph complex, Cartan connection, parabolic geometry
Annotation

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.