Speaker
Vjekoslav Kovač, University of Zagreb
Abstract
The branch of geometric measure theory that studies sets of positive Lebesgue measure differs from fractal geometry in that numerous typical questions are ruled out by the Lebesgue density theorem, prompting the search for stronger properties. However, its tools also typically come from harmonic analysis, and translation-invariant operators play a central role. We will provide a brief overview of standard problems and techniques, and then present some recent results on configurations found in every set of positive measure.