Jan Draisma

Associate Professor

Recreational Maths


October 2014: Rekha Thomas wrote a beautiful article for SIAM News on the Euclidean distance degree.

Fall 2014: The MEGA 2015 website is in place, and submission of papers, extended abstracts, computations, and posters is open!

October 2014: both my last-year's Master students have started Ph.D.'s: Jasmijn Baaijens in the CWI life sciences group, under the supervision of Alexander Schönhuth; and Guus Bollen in Discrete Maths here at TU/e, under the supervision of Hans Cuypers, Rudi Pendavingh, and myself. The best of luck to both!

September 2014: The conference website for the SIAM Conference on Applied Algebraic Geometry is up and running. Check it out, and consider organising a minisymposium! The conference has also been accepted as a ICIAM 2015 satellite.

July 2014: my Department nominated me for a TU/e Education Award, as their candidate in the category Best Master's Program Lecturer.

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 poly-time 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 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.


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 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)


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 e-mail to one of us.

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.