Geometric configuration in Euclidean, combinatorial and arithmetic settings
Vendredi 19 septembre 2008 - 14h00 - Salle Kampé de Fériet - M2
The following type of a problem has appeared persistently in ergodic theory, harmonic analysis, analytic number theory, geometric combinatorics and other areas. Let $E subset V$, where $V$ is a vector space. Suppose that $E$ is sufficiently large, in a suitable sense. Does it follow that $E$ contains a "copy" of your favorite geometric configuration? Making this notion precise leads to problems like Roth/Szemeredi theorem on arithmetic progressions, the Erdos distance problem, sum-product theorems in finite fields, the Falconer distance problem in geometric measure theory and many others. We shall describe some recent developments on these problems and connections between them.