Jan Draisma
Associate Professor
Contact
Publications
Programs
Talks
Teaching
Organisational
Recreational Maths
Links
News
Spring 2014: three members of the SIAM (AG)^2 were elected SIAM fellows: Jean Lasserre, Peter Olver, and Bernd Sturmfels. Congratulations!
24 February 2014: I wrote a guest post on Rota's basis conjecture for The Matroid Union.
9 January 2014: I won the GEWIS
teaching award 2013/2014 for Mathematics. Needless to say, I'm very, very
proud of this!
December 2013: I was elected Chair of the SIAM activity group on Algebraic
Geometry. This group brings together researchers who use algebraic
geometry in industrial and applied mathematics. If you are an algebraic
geometer interested in applications, or if you
have a maths/statistics/engineering/CS/... problem that you think might benefit from
algebraic techniques, please check out this activity group (or contact me). It's this interplay that makes the group such a success!
24 October 2013: my paper with Eggermont on the existence of polytime membership tests for a wide class of phylogenetic models has just been accepted for J. Eur. Math. Soc.
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 finitenessuptosymmetry results for
certain infinitedimensional toric varieties.
15 October 2012: the website of the CIME/CIRM course Combinatorial
Algebraic Geometry, taking place from 1015 June 2013 in Levico Terme,
is up. Check it out!
1 September 2012: Emil Horobeţ from BabesBolyai 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 Postdoc 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
This course is taught in Spring 2007, by Aart Blokhuis , Hans Cuypers and (a bit by) myself. See also
the course page at Mastermath.
Course material
Projective and Polar Spaces by Peter J. Cameron.
QMW Maths Notes 13.
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 crossratio (Section 4.5); application to
3designs. 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
To get ECTS points, we suggest that you write an essay on one of
these subjects.
DEADLINE for submission of essays: 26 August 2007, by email to one of us.
Further reading

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

A slowpaced 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.

Combinatoricstopics, 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.
