Simon Larson: A geometric uncertainty principle

One can decompose R^2 into disjoint sets of equal measure that are 'almost' disks (for instance hexagonal packing) and a Apollonian packing allows us to decompose the plane into disks of different sizes - it is however obvious that there are no partitions satisfying both properties.

In this talk I will try to quantify this statement in the form of a geometric uncertainty principle for partitions of sets in R^2. The talk is based on some recent work by Stefan Steinerberger.