Stieltjes Institute
Thomas Joannes Stieltjes (1856-1895)
Stieltjes afternoon October 8, 2010

On Friday October 8, 2010, there was a Stieltjes afternoon at Leiden University organized by the Thomas Stieltjes Institute for Mathematics.

Fred Bakker (l), Michiel Zonnevylle,
mayor of Leiderdorp (r)
During the meeting Paul van der Heijden, Rector Magnificus and Chairman of Leiden University,has presented to Peter van Heijster the Stieltjes Prize for the best Ph.D. thesis in 2009. After that there were presentations on the work of John Torrence Tate (University of Texas at Austin), who was awarded the Abelprize 2010 by the Norwegian Academy of Sciences "for his vast and lasting impact on the theory of numbers".

At the end of the afternoon Fred Bakker, secretary of the Stieltjes Institute, was appointed "Ridder in de Orde van Oranje-Nassau" for all his work in Mathematics and in the Stieltjes Institute.


13:15 -- 13:45
Welcome (coffee and tea)

Peter van Heijster (l) and
Paul van der Heijden (r)
13:45 -- 14:00
Presentation of the Stieltjes Ph.D.-student prize 2009
by Paul van der Heijden, Rector Magnificus and Chairman Leiden University.

14:00 -- 14:30
dr. Peter van Heijster (Brown University, USA), winner Stieltjes prize 2009
"Planar radial spots in a 3-component system"

14:45 --15:00
Prof.dr. Frans Oort (UU),
"John Tate: as a mathematician, as a person"

Jaap Top
15:00 --15:30
Prof.dr. Jaap Top (RUG),
"Tate and elliptic curves"

15:30 -- 16:00

Frans Oort
16:00 -- 16:30
Prof.dr. Frans Oort (UU),
"Tate modules and arithmetic geometry"

Peter Stevenhagen
16:30 -- 17:00 Prof.dr. Peter Stevenhagen (UL),
"Elliptic curves and cryptography"

17:00 -- 18:00

De Sitterzaal, Oortgebouw, Leiden University
Niels Bohrweg 2
2333 CA Leiden

If you would like to attend the Stieltjes afternoon you can send an e-mail to Tineke Bakker.

One research school
On January 1, 2011, the three research schools EIDMA, MRI and Stieltjes Institute will merge into one national research school mathematics.

dr. Peter van Heijster (Brown University, USA), winner Stieltjes prize 2009
"Planar radial spots in a 3-component system"
It is a well-accepted belief that the increase of the number of components in a reaction-diusion equation increases the complexity of the dynamics of the equation. In this presentation, we analyze the existence and stability of stationary localized structures of a certain two-dimensional three-component FitzHugh-Nagumo system. In particular, we report on results on the most unstable eigenvalues that decide through which type of instability the stationary structures become unstable. The underlying model was proposed in the nineties to describe, on a phenomenological level, the behavior of gas-discharge systems. Numerical simulations suggest that the third component is necessary to stabilize traveling spot solutions as these solutions are unstable for its two-component analogue.

Frans Oort (Universiteit Utrecht)
John Tate: as a mathematician, as a person
We will illustrate Tate's pioneering ideas in creating new tools, his modesty and his wit.

Jaap Top (Rijksuniversiteit Groningen)
Tate and elliptic curves
Tate's name is attached to a lot of notions and statements such as Tate-curve, Tate-cohomology, Tate-algorithm, Tate-pairing, (Barsotti-)Tate-group, Tate-module, Tate-conjectures, Tate-spectrum, (Lubin-)Tate formal group, (Sato-)Tate-equidistribution, and more. In this talk aimed at nonexperts we discuss some of Tate's influence on the theory of elliptic curves. Several of the notions mentioned above are related to this.

Frans Oort (Universiteit Utrecht)
Tate modules in arithmetic geometry
Classical tools like abelian integrals and lattices are of great use in complex geometry. However, in number-theoretic situations a new tool had to be invented. Tate constructed Tate modules, a very natural concept which started a great break-through in geometric aspects of number theory. We will show, on the one hand, how lattices and complex structures give strong results in complex geometry. These results have their natural analogues, on the other hand, in Tate modules and conjectures and results in arithmetic geometry. Tate showed the first important case: his conjecture for abelian varieties over finite fields. These ideas were later expanded by Faltings, and used in the proof of Wiles of FLT (although we will not discuss these). We will try to make both the classical analytic and the modern arithmetic ideas and analogies understandable for anyone.

Peter Stevenhagen (Universiteit Leiden)
Elliptic curves and cryptography

Tate's work is usually classified as being part of pure mathematics, and rightly so. The last few decades have however shown that there is no intrinsic distinction between pure and applied mathematics, and I will illustrate this by discussing the relevance of some of Tate's ideas in modern cryptography.

Organization Committee:
Fred Bakker
Frank den Hollander
Hendrik Lenstra
Peter Stevenhagen
  Thomas Stieltjes Institute for Mathematics
c/o Snellius
Leiden University
P.O. Box 9512
2300 RA Leiden
The Netherlands
Phone: +31 71 527 7042
Fax: +31 71 527 7101