Alex Scott, UCL

Reconstructing subsets of the plane

Abstract: How much information do we need to reconstruct (up to rigid motion) a finite set of points in the plane? Is it enough to know the collection (with multiplicities) of all its subsets of size k, given up to rigid motion? Is there some k that will suffice for every finite subset of the plane?

We present joint work with Luke Pebody and Jamie Radcliffe on the latter question, and discuss some related problems and conjectures.