per
il prossimo evento del ciclo dei Seminari di Analisi, giovedì
9 maggio alle ore 17:00, in Aula Riunioni, avremo il piacere di ascoltare Annalisa
Massaccesi
(Università di Padova), che
terrà un seminario dal
titolo “Recent developments on the Besicovitch's 1/2 problem ”.
Trovate qui sotto l’abstract.
Il
seminario sarà preceduto da una merenda dalle ore 16:45 nella stessa aula.
A
presto,
Ilaria Lucardesi
e Luigi Forcella
---------------------------------------------
Dear
all,
On
Thursday May 9th at
5PM, in "Aula Riunioni", for the Mathematical Analysis Seminar, we will have the pleasure of listening to Annalisa Massaccesi (Università di Padova). The
title of the talk is “Recent
developments on the Besicovitch's 1/2 problem ”.
Please find below the abstract.
The
seminar will be preceded by a snack in the same room, starting at 4:45 PM.
See
you soon,
Ilaria
Lucardesi and Luigi Forcella
---------------------------------------------
Speaker: Annalisa
Massaccesi (Università di Padova)
Title: Recent
developments on the Besicovitch's 1/2 problem
Abstract: The
Besicovitch's 1/2 problem 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+\sqrt{46})/12 ∼ 0.73186...
In a recent work in collaboration with C. De Lellis, F. Glaudo and D. Vittone, we devised 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.