Large sets with limited tube occupancy
Ciprian Demeter
Indiana University, Bloomington, USA
Abstract:
Split the unit square into $N^2$ congruent little squares.
Is there a choice of $N$ little squares such that each line of
arbitrary orientation intersects only $O(1)$ of them? This question is connected
to the hypothetical existence of bases of uniformly bounded spherical harmonics of
arbitrary degree on the two dimensional sphere. We discuss a few joint results with Ruixiang Zhang. The talk will be entirely elementary.