Zoë Pope

Zoë Pope

she/her

Mathematics graduate student

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portfolio

publications

Paper Title Number 4

Published in GitHub Journal of Bugs, 2024

This paper is about fixing template issue #693.

Recommended citation: Your Name, You. (2024). "Paper Title Number 3." GitHub Journal of Bugs. 1(3).
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talks

Rectifications of Homotopy Interleaving Distances

Published:

I gave this talk in the Applied Topology 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. In 2023, Andrew Blumberg and Michael Lesnick developed a universal homotopy interleaving distance. They additionally conjectured that this homotopy interleaving distance differed from the interleaving distance on a homotopy category by at most a multiplicative constant, which was later proved by Edoardo Lanari and Luis Scoccola. We cover the proof of this conjecture and detail the failure of this phenomenon for multi-persistent spaces.

The Randal-Williams–Wahl Machine

Published:

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 explore an axiomatization due to Oscar Randal-Williams and Nathalie Wahl of conditions on the groups \(G_n\) that imply homological stability, and show how this applies to classical groups of interest. We then explain Quillen’s spectral sequence argument and how it gives a proof of homological stability in the Randal-Williams–Wahl setup.

The Global Orbit Category and Assembly Maps

Published:

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

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

Adjunctions, Mates, and Kan Extensions

Published:

I gave this talk in the UAlbany Graduate Student Seminar.

Mates are a 2-categorical tool used to give elegant proofs for results about adjunctions. We first define adjunctions and then mates in the 2-category of all categories, and finally we demonstrate the power of the calculus of mates by proving results about left Kan extensions.

teaching