Codes and Expansions (CodEx) Seminar

Dustin G. Mixon (The Ohio State University):
Bilipschitz invariants

Motivated by problems in data science, we study the following questions:

1. Given a Hilbert space \(V\) and a group \(G\) of linear isometries, does there exist a bilipschitz embedding of the quotient metric space \(V/G\) into a Hilbert space?
2. What are necessary and sufficient conditions for such embeddings?
3. Which embeddings minimally distort the metric?

We answer these questions in a variety of settings, and we conclude with several open problems.