Zoë Pope

Zoë Pope

she/her

Mathematics graduate student

Talks

The Global Orbit Category and Assembly Maps

November 16, 2025

Talk, BUGCAT 2025, Binghamton, New York, USA

I gave this talk at the Binghamton University Graduate Combinatorics, Algebra, and Topology (BUGCAT) Conference in 2025.

We explored the global orbit ∞-category \(Orb\) of arbitrary discrete groups. We began by showing the orbit (1-)category \(\mathcal{O}(G)\) for a fixed \(G\) can be identified with the slice ∞-category \(Orb_{/G}\). We then used this equivalence to give purely categorical proofs for known results about assembly maps, like the transitivity principle.

The Randal-Williams–Wahl Machine

May 29, 2025

Talk, Talbot 2025, Cassopolis, Michigan, USA

I gave this talk at the Talbot 2025 workshop on homological stability, mentored by Alexander Kupers and Nathalie Wahl. My talk notes can be found here, and are mainly based off the original article by Randal-Williams and Wahl and Wahl’s ICM paper.

A sequence of groups \(G_1 \to G_2 \to \cdots\) exhibits homological stability if the induced maps on homology \(H_i(G_n) \to H_i(G_{n+1})\) are isomorphisms for \(n\) large relative to \(i\). In the talk, we explored an axiomatization due to Oscar Randal-Williams and Nathalie Wahl of conditions on the groups \(G_n\) that imply homological stability, and showed how this applies to classical groups of interest. We then explained Quillen’s spectral sequence argument and how it gives a proof of homological stability in the Randal-Williams–Wahl setup.

Rectifications of Homotopy Interleaving Distances

April 25, 2025

Seminar Talk, Albany ATiA Seminar, Albany, NY

I gave this talk in the Applied Toplogy in Albany Seminar.

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.