Séminaire Analyse-Proba (Annalisa Massaccesi, mardi 17 septembre)

Le prochain séminaire Analyse-Proba aura lieu mardi 17 septembre à 10h30 en salle A711. Annalisa Massaccesi (Università degli Studi di Padova) nous parlera de "Recent developments on Besicovitch's 1/2 problem."

Title : Recent developments on Besicovitch's 1/2 problem

Abstract
Besicovitch's 1/2 problem investigates the smallest threshold σ guaranteeing rectifiability for a set with Hausdorff 1-dimensional finite measure when the lower density of the set is larger than σ almost everywhere. Besicovitch conjectured that σ=1/2 (hence the name of the problem) and proved σ≦3/4, then Preiss and Tišer improved the bound to σ≦(2+√(46))/12~0.73186.... In a recent work in collaboration with C. De Lellis, F. Glaudo and D. Vittone, we devise a strategy to improve the bound by means of a hierarchy of variational problems and we reach a proof that σ≦0.7. In this seminar, I will try to explain the fairly intuitive geometric idea behind this strategy and I will try to summarize both the computational obstacles and the intrinsic obstacles that are still in the way.