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Projections of Polar Spaces

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In algebraic graph theory, the use of linear algebraic techniques applied to graphs consisting of vertices and edges, has been a major component in the study of strongly regular graphs; an area of modern mathematics which interests a wide variety of researchers.

Finite geometry is the study of incidence structures with a finite number of points, lines, planes, etc. The most important ambient objects are projective spaces, affine spaces, and polar spaces.

One of the dominant interests in recent times in finite geometry is in finding geometric models which yield strongly regular graphs and other important and related structures such as generalized quadrangles, (semi)partial geometries, and projective 2-weight codes.

Since the 1970's, geometers have not only succeeded in finding such rich models from polar spaces, but have also derived characterization and classification results, which give greater insight into this phenomena.

One of the central themes of this project is to introduce new techniques in order to complete these results and in particular to study the geometries arising from projecting a polar space embedded in a projective space onto a hyperplane of that space. The goal is to prove theorems in the same spirit as the ones that are known in the literature regarding a similar projection of generalized quadrangles.

Development of new techniques will be necessary, and in particular the use of group theory, the mathematical study of symmetry, will be utilised. Also included in this study is an investigation into embeddings of (semi)partial geometries into affine spaces, begun in the works of De Clerck, Delanote, De Winter, and De Feyter.

Wissenschaftliches Gebiet (EuroSciVoc)

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Thema/Themen

Aufforderung zur Vorschlagseinreichung

FP6-2005-MOBILITY-7
Andere Projekte für diesen Aufruf anzeigen

Finanzierungsplan

IIF - Marie Curie actions-Incoming International Fellowships

Koordinator

UNIVERSITEIT GENT
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