Research

My research is in equivariant homotopy theory.

My thesis focuses on the algebraic structure of twisted topological Hochschild homology (THH) and the twisted Bökstedt spectral sequence.

I am also in a Women in Topology (WIT) group with Kristen Mazur, Angélica M. Osorno, Constanze Roitzheim, Rekha Santhanam, and Valentina Zapata Castro. Our group works in homotopical combinatorics, studying the relationship between homotopy theory and combinatorics through transfer systems.

Preprints and Publications

On the Tambara affine line

David Chan, David Mehrle, J.D. Quigley, Ben Spitz, and Danika Van Niel

Submitted. arXiv: 2410.23052


Uniquely compatible transfer systems for cyclic groups of order p^{r}q^{s}

Kristen Mazur, Angélica M. Osorno, Constanze Roitzheim, Rekha Santhanam, Danika Van Niel, and Valentina Zapata Castro

To appear in Topology and its applications. arXiv: 2401.13523

Some Past Presentations

Algebraic Geometry of Tambara Functors

JMM Slides - January 2025

JMM TS.pdf

Lesser Simply Paired Transfer Systems

JMM Slides - January 2024

JMM twTHH.pdf

Algebraic structures of twisted topological Hochschild homology

JMM Slides - January 2024

Computational Approaches to Twisted Topological Hochschild Homolgoy.pdf

Computational approaches to twisted topological Hochschild homology

UPenn Homotopy Seminar - April 2023 (Note that this was not meant to be a slide talk)

Hochschild Homology for Green Functors.pdf

Hochschild homology for Green functors

eCHT Equivariant Algebra Reading Seminar - April 2021

Poster for my University of Kentucky Math Club talk - Made by Sydney Yeomans, pictures by Maxine Calle (as seen in this article)