## Research

### Work in progress

**A contracting flow on the stability manifold in type \(A\)** (with Anand Deopurkar, Anthony Licata)

In progress.

**Talks:** QUACKS II 2022

**The sphere of spherical objects** (with Anand Deopurkar, Anthony Licata)

In progress.

**Talks:** Davis 2022 (slides), LAGOON 2022 (slides), AustMS 2021 (slides)

### Papers

**Spherical objects and stability conditions on 2-Calabi–Yau quiver categories** (with Anand Deopurkar, Anthony Licata)

Mathematische Zeitschrift 303, 13 (2023).

**Talks:** FD Seminar 2022 (slides), GPRT seminar 2022 (notes)

**Computing the matching distance of 2-parameter persistence modules from critical values** (with Robyn Brooks, Claudia Landi, Celia Hacker, Barbara Mahler, Elisabeth Stephenson)

Preprint.

(arXiv)

**Morse-based fibering of the persistence rank invariant** (with Robyn Brooks, Claudia Landi, Celia Hacker, Barbara Mahler)

Research in Computational Topology 2 (2022), pp. 27–62

**\(q\)-deformed rational numbers and the 2-Calabi–Yau category of type \(A_{2}\)** (with Louis Becker, Anthony Licata)

To appear in Forum of Mathematics, Sigma.

**Talks:** Sydney 2022 (slides), MIT 2022 (slides), Paris 2022 (slides), ICERM 2022 (slides), DiTS 2021 (slides, video)

**A Thurston compactification of the space of stability conditions** (with Anand Deopurkar, Anthony Licata)

Submitted.

**Talks:** FD Seminar 2022 (slides), DiTS 2021 (slides, video), AMS special session 2021 (slides), RepNet 2021 (video), UGA 2020 (slides), Mooloolaba 2020 (slides)

**Recollement for perverse sheaves on real hyperplane arrangements**

Journal of Algebra, 568 (2021), pp. 61–90

**Talks:** Melbourne 2018 (notes)

**The strong topological monodromy conjecture for Coxeter hyperplane arrangements** (with Robin Walters)

Mathematical Research Letters 24 (2017), no. 4, 947–954

**Talks:** JMM 2017 (slides)

**Torus actions and tensor products of intersection cohomology**

Pacific Journal of Mathematics 276 (2015), pp. 19–34

**Talks:** AMS special session 2017 (slides)

**Lower central series of free algebras in symmetric tensor categories** (with David Jordan)

Journal of Algebra, 373 (2013), pp. 299–311

### Not for publication

**Equivariant cohomology and the localization theorem**

Topic proposal (expository).

(pdf)

**The Bernstein-Sato \(b\)-function of the Vandermonde determinant** (with Robin Walters)

Preprint (not for publication).

(arXiv)

### Code

**Categorical braid group actions** (with Anand Deopurkar)

This sage code computes the braid group action on the triangulated category of complexes of projective modules over the zig-zag algebra of a quiver.

(github)