News

1 May 2013: my paper with Kuhnt and Zwiernik on groups acting on Gaussian graphical models has just been accepted for Annals of Statistics.

Spring 2013: Robert Krone from GeorgiaTech is visiting for three months. Together with Anton Leykin and Rob Eggermont we aim to prove finiteness-up-to-symmetry results for certain infinite-dimensional toric varieties.

15 October 2012: the website of the CIME/CIRM course Combinatorial Algebraic Geometry, taking place from 10-15 June 2013 in Levico Terme, is up. Check it out!

1 September 2012: Emil Horobeţ from Babes-Bolyai university joins the group on the project Tensors of Bounded Rank.

23 January 2012: Tensors of Bounded Rank, an NWO free competition Ph.D. project proposal together with Monique Laurent and Siep Weiland has been awarded funding!

23 January 2012: Piotr Zwiernik is starting a Post-doc in the Vidi project.

1 September 2011: Rob Eggermont started his Ph.D. in the Vidi project.

2 March 2011: a manuscript with Johan P. de Jong on his Bachelor's project has been accepted for publication in the EMS Newsletter. See this page.

6 October 2010: A Vidi grant! See this page or this page or this page.

Teaching

Discrete Structures

Course material

Summary of the topics treated thus far in the course

Week 1

Introduction to fields and vector spaces and finite projective planes. Wedderburn's theorem.

Week 2

Collineations. The fundamental theorem of projective geometry. The Desargues configuration.

Week 3

Counting subspaces and determining group orders. Coordinatisation of projective spaces of order 2.

Week 4

Affine spaces. Transitivity of parallelism. (Sections 3.5 and 3.6 of the course material). Spreads and translation planes (Section 4.1). Segre's theorem (Section 4.3).

Week 5

The projective line and cross-ratio (Section 4.5); application to 3-designs. Baer subplanes, and Aiden Bruen's theorem. Blokhuis's theorem (without proof).

Week 6

Dualities and polarities of projective spaces and sesquilinear forms (Section 6.1 and 6.2).

Week 7

Polarities and related forms and their geometry (remaider chapter 6).

Week 8

Polar spaces, an axiomatic approach (chapter 7)

Subjects

Further reading

Projective Geometry by Albrecht Beutelspacher and Ute Rosenbaum. Cambridge University Press, 1998.

A slow-paced elementary treatment for readers with little mathematical background.

Designs, Graphs, Codes, and their Links by Peter J. Cameron and J.H. van Lint. London Math. Soc. Student Texts.

For people interested in design theory, partial geometries, and their relation to finite projective planes.

Miniquaternion Geometry by T.G. Room and P.B. Kirkpatrick. Cambridge University Press, 1971.

An introduction to the study of projective planes with emphasis on the four different planes of order 9, their coordinatisation, and the study of substructures such as ovals, Hermitian sets and subplanes.

Finite Geometries by Peter Dembowski. Springer Verlag, 1968 (reprinted 1979).

The classic treatment of the combinatorics of finite projective and affine planes and their classification in terms of groups acting on them.

Combinatorics---topics, techniques, algorithms by Peter J. Cameron. Cambridge University Press.

Contains a very readable introductory chapter on finite geometry.

Projective geometries over finite fields by J.W.P. Hirschfeld. Oxford University Press.

A very useful collection of results on combinatorial structures in projective planes such as arcs, ovals, cubic curves, blocking sets; and a special chapter on the planes of orders 2,3,...,13.

Projective Planes by Daniel R. Hughes and Fred C. Piper. Springer Verlag.

Elaborate study of the algebraic structures that are used to coordinatise the different kinds of finite projective planes.

Eindige Meetkunde by J.J. Seidel.

Lecture notes in Dutch. Contains all the basics and an elaborate treatment of quadratic and hermitian forms, as well as an introduction to polar spaces.