Broadly, my area of interest is algebraic topology and stable homotopy theory. In this field, we study spaces using algebraic tools, such as cohomology theories. We also study the cohomology theories themselves and the relationships between them. I am particularly interested in the equivariant case, where the cohomology theories are designed to work with the action of a symmetric group.

On a more specific level, I study the algebra arising in equivariant stable homotopy theory and the structure of the equivariant stable category. This includes phenomena such as "norm multiplications" which come from equivariant commutative ring spectra. I am also interested in ways of building equivariant spectra from algebraic data, and in understanding to what extent we can think of algebra as determining such spectra.

A second area of interest is K-theory, both topological and algebraic, and cohomology theories connected to K-theory. For example, I am interested in the structural properties of algebraic K-theory constructions. Current work also involves algebraic strucure on cohomology theories related to K-theory, such as topological coHochschild homology.

Papers and preprints

Topological coHochschild homology and the Homology of Free Loop Spaces (arXiv). Joint with Teena Gerhardt, and Brooke Shipley.

Assembly and Morita invariance in the algebraic K-theory of Lawvere theories (arXiv). Joint with Markus Szymik.

Genuine-commutative structure on rational equivariant K-theory for finite abelian groups (arXiv). Joint with Christy Hazel, Jocelyne Ishak, Magdalena Kędziorek and Clover May.

Naive-commutative structure on rational equivariant K-theory for abelian groups (arXiv). Joint with Christy Hazel, Jocelyne Ishak, Magdalena Kędziorek and Clover May. Accepted for publication in Top. Appl.

A multiplicative comparison of Waldhausen and Segal K-theory Joint with Angélica Osorno. Mathematische Zeitschrift 295, 1205– 1243. 2020.

Graded Tambara Functors. Joint with Vigleik Angeltveit. J. Pure Appl. Algebra 222 (2018), no. 12, 4126– 4150.

Computational tools for topological coHochschild homology Joint with Teena Gerhardt, Amelia Hogenhaven, Brooke Shipley, and Stephanie Ziegenhagen. Topology and its Applications. Vol 235, 15 February 2018, pp. 185 – 213.

Constructing equivariant spectra via categorical Mackey functors. Joint with Angélica Osorno. Algebraic and Geometric Topology. 15 (2015) 537–563.

A model structure on GCat. With Kristen Mazur, Angélica Osorno, Viktoriya Ozornova, Kate Ponto and Carolyn Yarnall. Contemporary Math Volume 641, 2015.

Global orthogonal spectra. Homology, Homotopy and Applications. Vol 16 (2014), No 1, 313-332.

A comparison of norm maps. With appendix by Anna Marie Bohmann and Emily Riehl. Proceedings of the American Mathematical Society 142 (2014), 1413-1423.

A presheaf interpretation of the generalized Freyd Conjecture. Joint with Peter May. Theory and Applications of Categories 26 (2012), 403-411

The Equivariant Generating Hypothesis. Algebraic & Geometric Topology 10 (2010) 1003–1016

Link to my papers on the arXiv.

Slide presentations

The S1-equivariant Generating Hypothesis (pdf), presented at the AMS Special Session on New Trends in Triangulated Categories, October 24-25, 2008.

Informal Notes

Basic notions in equivariant stable homotopy theory (pdf)(dvi), notes from a January 20, 2010 talk in the University of Chicago Topology Proseminar. Several typos corrected July 2012, thanks to Mona Merling.

Notes from the February 2012 BIRS workshop on Algebraic K-theory and equivariant homotopy theory .