Zoltán Buczolich (ELTE): Purely unrectifiable sets, fractal percolation and graphs of functions

In this talk, I will survey some of my results related to unrectifiability. These include irregular/purely unrectifiable 1-sets on the graphs of continuous functions like the Takagi, the Weierstrass-Cellerier and the typical (in the sense of Baire) continuous function. Moreover, I will also discuss the fact that the fractal percolation is almost surely purely α-unrectifiable for all α > α0. This latter result is from a joint paper with Esa Järvenpää, Maarit Järvenpää, Tamás Keleti and Tuomas Pöyhtäri. This lecture is based on my slides prepared for the Second Winter School in Geometric Measure Theory: Rectifiability vs. Pure Unrectifiability, Westlake University, Hangzhou, China.