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Research

Maximal compatibility of disklike G-transfer systems, with David DeMark, Mike Hill, Nelson Niu, Kurt Stoeckl, Danika Van Niel, and Guoqi Yan; preprint (2026)

The homotopy fixed points of Real spin bordism, with Hassan Abdallah; preprint (2025)

On the nonexistence of a Green functor with values spinc bordism and spin bordism, with Hassan Abdallah and Zachary Halladay; Archiv der Mathematik (2026)

Real spin bordism and orientations of topological K-theory, with Zachary Halladay; Transactions of the American Mathematical Society (2026)

Generalizations and strengthenings of Ryser's conjecture, with Louis DeBiasio, Grace McCourt, and Hannah Sheats; Electronic Journal of Combinatorics (2021)


Expository notes

A guide to the literature on topological K-theory (in progress, last edit: November 2025)
An ongoing project to assemble a concise yet thorough categorized map of the literature on topological K-theory. The goal is to make it easy to learn what is known and where various things are discussed.

Strong monoidal functors and modules (2023)
While trying to sort out varying Clifford algebra sign conventions in the literature, I wanted to know that a strong monoidal functor which is an isomorphism of categories preserves categories of modules. I couldn't find this fact anywhere, so I wrote up a proof. A similar fact holds for equivalences of categories.

Twisted equivariant K-theory (2022)
Notes for a talk given on 10/24/22 in this seminar.

Equivariant K-theory (2022)
Notes for a talk given on 9/19/22 in this seminar.

The (strict) 2-category of categories (2022)
A detailed proof that categories, functors, and natural transformations form a strict 2-category.


Other documents

Stories about Friedhelm Waldhausen (by members of the algebraic topology community)
A collection of thoughts and stories about Waldhausen that were shared by members of the alg-top email list.