Title: Analytic capacity and Favard length
Abstract: Favard length of a planar set is the average length of its
orthogonal projections. The Besicovitch projection theorem, which is one
of the cornerstones of geometric measure theory, states the following:
if a set E of finite length has positive Favard length, then there
exists a rectifiable curve intersecting E in a set of positive length.
In this talk I will discuss my recent quantification of this classical
result, and its application to Vitushkin's conjecture.
