Title : Covering the Sierpinski carpet by tubes

Speaker:  Prof. Meng Wu ( The University of Oulu )

Time: Fri, Dec.11 2020, PM:16:00-17:00

Location: Tencent Conference

Meeting  Number: 836 147 469

Password: 654321

Inviter: Prof. Bing Li

Abstract:

       A planar set is called tube-null if it can be covered by a union of tubular neighbourhoods of lines with the sum of their widths arbitrarily small. Such sets arise in the localization problem for the Fourier transform. Any set of finite one-dimensional Hausdorff measure is easily seen to be tube-null, but it is often hard to determine whether a given set of dimension larger than 1 is tube-null or not. In particular, there were very few (non-trivial) examples of tube-null sets of large dimension. I will present our recent result, joint with A. Pyörälä, P. Shmerkin and V. Suomala, that the Sierpinski carpet is tube null. More generally, any times-N invariant set other than the torus is tube-null.