@Stat PhD Now Postdoc thanks for the discussion. It really is helping, especially given the really tight timing.
Given what you've said above, I understand a subfield such as topological data analysis (TDA) uses mathematical tools such as algebraic topology to then apply to data/statistics. In that regard, UW has people like Marina Meila who has worked on Manifold Learning, and Yen-Chi Chen who has some work on applied algebraic topology for statistical inference. At Princeton in terms of TDA and related fields, I can only find Ramon van Handel who has done work on the geometry of probability.
If I want to do research in fields as close as possible to TDA and its applications to statistics, I'm leaning towards UW currently over Princeton. Do you think that is a relatively correct assessment?