Bilipschitz invariants

School of Mathematics Colloquium
Thursday, February 15, 2024 - 11:00am for 1 hour (actually 50 minutes)
Skiles 005
Dustin Mixon – Ohio State University – mixon.23@osu.edu
Alex Dunn

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.