Getaltheorie in het
Journées estivales de la Méthode Polynomiale
24-27 juin, 2013
Lieu : LPP, Salle de Réunion
When dealing with an interesting sequence, one of the standard approaches
is to encode the sequence under consideration into a generating function.
Sometimes this yields just a simplified way of expressing relations,
sometimes methods from other parts of mathematics, mostly complex analysis, become applicable.
Less known is the non-archemidean analogue of this approach,
the so called polynomial method. To study an interesting finite set,
we here encode this set into a polynomial, and apply theorems from algebraic geometry such as the combinatorial Nullstellensatz or the Chevalley-Warning-theorem.
In finite geometry the first successful application known to us is due to
Rédei, who constructed what is today known as the Rédei-polynomial
while in additive combinatorics this method was used by Hamidoune and Alon among others.
In recent conferences we noted that people working in finite geometry
do not know about additive combinatorics and vice versa, and that the polynomial method was also successfully applied to other fields of discrete mathematics, in other words, that different circles used the same theorems in a similar way without knowing each other. It is the aim of the present conference to create contacts between these circles.
While large parts of the archemidean theory can be formalized and largely mechanized, the polynomial method requires more skill in the construction of the polynomials and the interpretation of the results. This may come as a disappointment to the working mathematician, who cannot rely on a ready-made toolbox, on the other side it is encouraging as it increases the chances of surprising new proofs. We hope that the present conference helps increase these chances.
(Click on names for lectures)
Paul Baginski (Northampton)
Éric Balandraud (Paris)
Jan de Beule (Gand)
Arnaud Bodin (Lille)
Satwik Mukherjee (Lille)
Alain Plagne (Paris)
Christian Reiher (Hamburg)
Uwe Schauz (Suzhou)
Wolfgang A. Schmid (Paris)
Leo Storme (Gand)
Tamás Szőnyi (Budapest)
que tous les auditeurs s'inscrivent.