Codes and Expansions (CodEx) Seminar

Steven Gortler (Harvard University):

Invariant Embeddings

Fix a dimension \(d\) and graph \(H\), with \(n\) vertices and \(m\) edges. Let \(p\) be a configuration of \(n\) points in \(R^d\).Then we can measure the configuration, mod the Euclidean group, by recording the squared length between eachpoint pair associated with an edge of \(H\). When \(H\) is generically globally rigid in d-dimensions, then this measurementmap is an almost everywhere injective map from \(R^{nd}/E(d)\) to \(R^m\). In this talk, I will discuss the general question of howwe can create fully injective maps  from \(R^{nd}/G\) to \(R^m\) where \(G\) is some group and \(m\) is roughly \(2nd\).

This is work with Nadav Dym.