Monthly Archives: April 2011

Petition: Save Geometry from the threat at VU Amsterdam

Please read the following message from Rob de Jeu, and sign the petition via the link below. The text of the petition is reproduced beneath the link. — Burt Totaro

My university (VU University Amsterdam) has put forward a plan to close the Geometry Section of the department of mathematics. This means that 4 mathematicians (Dietrich Notbohm, Tilman Bauer, Jan Dijkstra and me) will lose their jobs, creating a department with only stochastics and analysis. You can help us by signing the petition below by clicking on the link and follow the necessary steps.

Feel free to forward this message. We need your help now. Only if many mathematicians will protest, this may have an effect.

Best wishes, Rob.

As with most universities in the Netherlands, the VU University Amsterdam suffers from financial underfunding. All faculties and all departments at the VU are asked to take measures to deal with this problem. For the Department of Mathematics a committee of applied mathematicians has put forward a proposal to close the Geometry Section, which consists of six tenured positions and focuses on algebraic K-theory, algebraic topology, and general/geometric topology. At the same time, some of the funds freed up by the abolition of the Geometry Section are to be used for the creation of two additional positions in the Analysis Section. This proposal has received the endorsement of the Dean of the Faculty of Sciences and of the Executive Board of the university. Two members of the Geometry Section will retire in the next two years and closure of the section will allow for termination of the other four tenured positions. Thus, the proposal’s drastic measures will merely cut the total number of positions by two.

Of the four positions slated for termination, one is in general/geometric topology and has been held since 2001 by Jan Dijkstra. The other three people were appointed less than four years ago: Dietrich Notbohm, Rob de Jeu, and Tilman Bauer. This introduced algebraic K-theory and algebraic topology as new research subjects at the VU. In 2010, a research evaluation of all Dutch mathematics departments by an international committee took place. The committee welcomed these changes very much, stating that strong young people provided new impetus to the group in mainstream mathematics and offered promise for the future.

What are the consequences of the closure of the Geometry Section for the university? Algebra, algebraic topology, and general/geometric topology will vanish. Algebraic K-theory and general/geometric topology will cease to exist in the Netherlands, and only Utrecht will be left with research in algebraic topology. No pure mathematicians will be on the staff anymore. The university will give up central areas of mathematics and adopt a narrow research profile. The education of students offered at the VU will also become much narrower, which may lead to a drop in the yearly intake of students, and will certainly compromise the academic chances for VU graduates.

This petition asks for a reconsideration of this plan. By signing it you will help to save the Geometry Section at the Department of Mathematics at the VU!

I appeal to the Department of Mathematics, the Faculty of Sciences, and the Executive Board of the VU University Amsterdam to repeal the plan to close the Geometry Section. Proceeding with the proposal as it stands would severely damage the quality of research and teaching in mathematics at the VU. Laying off capable tenured faculty and hiring new faculty at the same time is intolerable.

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Paper: Pseudo-abelian varieties

I’ve posted this paper on the ArXiV: arXiv:1104.0856v1 [math.AG]


Chevalley’s theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect. We define a pseudo-abelian variety over an arbitrary field k to be a smooth connected k-group in which every smooth connected affine normal k-subgroup is trivial. This gives a new point of view on the classification of algebraic groups: every smooth connected group over a field is an extension of a pseudo-abelian variety by a smooth connected affine group, in a unique way.

We work out much of the structure of pseudo-abelian varieties. These groups are closely related to unipotent groups in characteristic p and to pseudo-reductive groups as studied by Tits and Conrad-Gabber-Prasad. Many properties of abelian varieties such as the Mordell-Weil theorem extend to pseudo-abelian varieties. Finally, we conjecture a description of Ext^2(G_a,G_m) over any field by generators and relations, in the spirit of the Milnor conjecture.

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Warwick talk: Algebraic geometry from a topological point of view

I will be speaking at the Young Researchers in Mathematics conference, at Warwick, Saturday 16th April, 10:15-11:15. A few weeks ago I provided a short, workmanlike abstract:

We discuss the role of topology in algebraic geometry. There are simple but surprising arguments which show that many properties of a complex submanifold of projective space are controlled by its topology, in fact by the second homology group. More subtle properties are determined by a convex cone, the “cone of curves”. For algebraic surfaces, the cone of curves can be studied using hyperbolic geometry.

This description now looks a little dull to me. So why, if you’re a young researcher in mathematics, should you come to my talk? Here’s an abstract that describes the point of the talk rather than just summarizing its technical content:

In algebraic geometry, questions — e.g. can I deform this curve? — seem to have stark yes-or-no answers. This binary landscape is far from the real picture. Topology — in particular, obstruction theory — gives us a language and framework for more calibrated answers. Using topology, when the answer is no, we can describe how far from yes it is. When the answer is yes, we can understand why and by how much. Obviously, this is useful if you’re an algebraic geometer. If you’re not an algebraic geometer, the example of topology’s value in algebraic geometry may be suggestive of the benefits for you of knowing some topology.

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