From orthogonal projections to Furstenberg sets


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.

06 Sep 2022 15:00
Damian Dąbrowski
Damian Dąbrowski
Postdoc in mathematics

My research interests include geometric measure theory and harmonic analysis.