From orthogonal projections to Furstenberg sets

Abstract

Given $0<s<1$ and $0<t<2$, we say that a planar set $F$ is an $(s,t)$-Furstenberg set if there exists a $t$-dimensional family of affine lines such that the intersection of $F$ with each line in the family is at least $s$-dimensional. The Furstenberg sets are fractal generalizations of Besicovitch sets, and obtaining lower bounds for their Hausdorff dimension is a major open problem. In this talk I will discuss some new estimates obtained by studying orthogonal projections of Frostman measures. Based on joint work with T. Orponen and M. Villa.

Damian Dąbrowski

Postdoc in mathematics

My research interests include geometric measure theory and harmonic analysis.