Research

Computing algebraic invariants in equivariant, motivic, and chromatic homotopy theory is the primary focus of my work in algebraic topology.  Interest in these invariants arises from the fact they they can often be applied to yield solutions to deep problems in geometry, topology, and algebra. 

You can read more in my research statement (updated 2025 materials coming soon!).

Algebraic Topology Publications

1. The real Brown-Peterson homology of Ω⍴S⍴+1, with Christian Carrick and Bertrand Guillou 

(preprint coming soon! - Fall 2025)

2. Splittings of truncated motivic Brown-Peterson cooperations algebras, with Jackson Morris, and Elizabeth Tatum

Submitted. arXiv:2509.19542

3. A spectrum-level splitting of the  kuR -coopertations algebra, with Guchuan Li and Elizabeth Tatum

Submitted.  arXiv:2503.17149 (talk slides, video)

4. Equivariant Witt Complexes and Twisted Hochschild Homology, with Anna Marie Bohmann, Teena Gerhardt, Cameron Krulewski, and Lucy Yang 

Topology and its Applications 2025, 109444, ISSN 0166-8641. arXiv:2409.05965

5. A Thom Spectrum Model for C2-Integral Brown-Gitler Spectra, with Guchuan Li and Elizabeth Tatum 

Proceedings of the American Mathematical Society, to appear.  arXiv:2308.12945

6. The HF2 - Homology of C2- Equivariant Eilenberg-MacLane Spaces 

Algebraic & Geometric Topology 24 (2024) 4487-4518. (arXiv:2206.08165, talk slides)

Publications with undergraduates

7.  Graphs arising from the dual Steenrod algebra, with Connor Elliott, Courtney Hauf, Kai Morton, and Leticia Schow

Submitted.  arXiv:2508.17041

8. A Gallery of Theorems, with Cody Dicesare, AJ Jelonnek, Clyde Kertzer, and Ella Tod 

Math Horizons, 33(1), 10–13. https://doi.org/10.1080/10724117.2025.2503129 

9. Talk slides - A Geometric Equivalence of Delooping Machines, with Olivia Dalfollo-Daley, Ileana Hills, Amelia Shawn Huxtable, Taylor Rogers, and Austin Walsh

Other scientific publications

10. Quantitative Microbial Risk Assessment of Swimming in Sewage Impacted Waters Using CrAssphage and Pepper Mild Mottle Virus in a Customizable Model, with Katherine Crank and Kyle Bibby 

Environmental Science & Technology Letters 2019 6 (10), 571-577.

11. modeLLtest: An R Package for Unbiased Model Comparison using Cross Validation, with Shana Scogin and Jeffrey J. Harden

Journal of Open Source Software 2019 4(41), 1542.

Fun: A very important dg - cat