(1) Colloquium : ? In this first talk we shall describe some general principles in the theory of Lebesgue differentiation, see how the validity in general frameworks of a Lebesgue-type differentiation theorem relates to property of some associated operator, before to focus our attention on the delicate issue of differentiating along rectangles ?.

(2) Lectures : ? After recalling some classical material from Harmonic Analysis and basic Geometric Measure Theory, we shall start by some general necessary and sufficient conditions on a sequence of averaging operators, in order for them to converge almost everywhere in a given function space. This will allow us to discuss interesting positive and negative results for ergodic, Lebesgue and convolution averaging processes.

Host: Prof. Thierry De Pauw