Mathematics

There are many ways to give a size of a set in $R^n$. The concept of fractal dimension allow us to differentiate between those sets that are indistinguishable for the Lebesgue measure. In this talk we will discuss the following question: How small can a set be if it contains a scaled copy of a given set around a large set of points of $R^n$? Also, we will try to see how can to treat these kind of problems from the point of view of harmonic analysis, for example, using maximal operators.