Zoë Pope

Zoë Pope

she/her

Mathematics graduate student

Talks

Homological Stability of Automorphism Groups

May 29, 2025

Talk, Talbot 2025, Cassopolis, Michigan, USA

This talk was given as part of attendance in Talbot 2025, centered on the topic of homological stability. I gave motivation and set up the axiomatization of proving homological stability in a range for a given sequence of groups satisfying some properties. First, the general setting of braided monoidal groupoids were introduced followed by giving its `space of destabilizations’ needed to apply Quillen’s spectral sequence argument.

Rectifications of homotopy interleaving distances

April 25, 2025

Seminar Talk, Albany ATiA Seminar, Albany, NY

Topological data analysis employs an `interleaving distance’ between persistence spaces as a means of measuring when two such objects are approximately isomorphic. By generalizing this notion to homotopy interleavings, one can instead measure when persistent spaces are approximately weakly equivalent. Michael Lesnick and Andrew Blumberg developed a universal homotopy interleaving distance and conjectured that it differed from the interleaving distance on a homotopy category by at most a multiplicative constant. The conjecture was later proved by Edoardo Lanari and Luis Scoccola. I gave motivation and proof of this conjecture, stating the homotopy interleaving distance on \(\textnormal{Fun}(\mathbb{Z},Spc)\) is within a multiplicative constant of the interleaving distance on \(\textnormal{Fun}(\mathbb{Z},\textnormal{Ho}(Spc))\). I also detailed the failure of this phenomenon for multi-persistent spaces.