### Research Focus

Algebraic topology and algebraic K-Theory

My research focuses on three programs:

- Computing the classical, equivariant, and motivic stable homotopy groups of spheres.
- Using stable homotopy theory to understand algebraic K-theory, topological cyclic homology, and related invariants.
- Developing the algebra of Mackey and Tambara functors.

Broadly speaking, these projects are motivated by classification problems in geometry, topology, and algebra, such as the classification of spheres up to diffeomorphism, aspherical manifolds up to homeomorphism, or symmetric bilinear forms up to equivalence.

### Publications

Real motivic and C

_{2}-equivariant Mahowald invariants. J. Topol. 14-2 (2021), 369-418.kq-resolutions I (with Dominic Culver). Trans. Amer. Math. Soc. 374-7 (2021), 4655-4710.

Motivic Mahowald invariants over general base fields. Doc. Math. 26 (2021), 561-582.

The Segal Conjecture for topological Hochschild homology of the Ravenel spectra (with Gabriel Angelini-Knoll). J. Htpy. Rel. Str. 16-1 (2021), 41-60.

The motivic Mahowald invariant. Alg. Geom. Topol. 19-5 (2019), 2485-2534.

tmf-based Mahowald invariants. To appear in Alg. Geom. Topol. arXiv:1911.07975.