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 Prof.mr. 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 OranjeNassau" for all his work in Mathematics and in the Stieltjes Institute.
PROGRAMME
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 Prof.mr. 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 3component 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
Break
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
DRINKS
Location:
De Sitterzaal, Oortgebouw, Leiden University
Niels Bohrweg 2
2333 CA Leiden
Registration
If you would like to attend the Stieltjes afternoon you can send an email 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.
ABSTRACTS
dr. Peter van Heijster (Brown University, USA), winner Stieltjes prize 2009
"Planar radial spots in a 3component system"
It is a wellaccepted belief that the increase of the number of components in a reactiondiusion 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 twodimensional threecomponent FitzHughNagumo 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 gasdischarge systems. Numerical simulations suggest that the third component is necessary to stabilize traveling spot solutions as these solutions are unstable for its twocomponent 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 Tatecurve, Tatecohomology, Tatealgorithm, Tatepairing,
(Barsotti)Tategroup, Tatemodule, Tateconjectures, Tatespectrum,
(Lubin)Tate formal group, (Sato)Tateequidistribution, 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 numbertheoretic
situations a new tool had to be invented. Tate constructed Tate
modules, a very natural concept which started a great breakthrough
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
