2024 FFT

Bilipschitz invariants

Dustin Mixon (OSU)

Abstract: 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.