SUBJECT
Title
Finite geometries
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
The axiomams of projective and affine planes, examples of finite planes, non-desarguesian planes. Collineations, configurational theorems, coordinatization of projective planes. Higher dimensional projective spaces.
Arcs, ovals, Segre’s Lemma of Tangents. Estimates on the number of points on an algebraic curve. Blocking sets, some applications of the Rédei polynomial. Arcs, caps and ovoids in higher dimensional spaces.
Coverings and packings, linear complexes, generalized polygons. Hyperovals.
Some applications of finite geometries to graph theory, coding theory and cryptography.
Readings
- Hirschfeld, J:W.P.: Projective Geometries over Finite Fields, Clarendon Press, Oxford,1999.
- Hirschfeld, J.W.P.: Finite Projective Spaces of Three Dimensions, Clarendon Press, Oxford, 1985.