Research

My work focuses on invariants of ring spectra that shed light on arithmetic and geometry.

Published papers

• Geometry & Topology Algebraic K-theory of elliptic cohomology.
  Joint with Ch. Ausoni, D. L. Culver, E. Höning, and J. Rognes. Publication

• Algebraic & Geometric Topology Topological Hochschild homology of the second truncated Brown-Peterson spectrum I. Joint with D. L. Culver and E. Höning. Publication

• Homology, Homotopy and Applications Complex orientations of TP of complete DVRs. Publication

• Transactions of the American Mathematical Society Detecting beta elements in iterated algebraic K-theory of finite fields. Publication

• Journal of Topology On topological Hochschild homology of the K(1)-local sphere. Publication

• Journal of Homotopy and Related Structures The Segal Conjecture for Topological Hochschild Homology of Ravenel spectra. Joint with J.D. Quigley. Publication

• Algebraic & Geometric Topology A May-type spectral sequence for topological Hochschild homology. Joint with A. Salch. Publication

Submitted Papers

• Syntomic cohomology of Morava K-theory. Joint with J. Hahn and D. Wilson. arXiv

• Topological Delta G-homology of twisted G-rings. Joint with M. Merling and M. Peroux. arXiv

• Algebraic K-theory of real topological K-theory. Joint with Ch. Ausoni and J. Rognes. arXiv

• A deformation of Borel equivariant homotopy. Joint with M. Behrens, E. Belmont, and H. J. Kong. arXiv

• Real Topological Hochschild homology via the norm and Real Witt vectors. Joint with T. Gerhardt and M. A. Hill. arXiv

• Commuting unbounded homotopy limits with Morava K-theory. Joint with A. Salch. arXiv

• Chromatic complexity of algebraic K-theory of y(n). Joint with J.D. Quigley. arXiv l

Notes

1. Maps of simplicial spectra whose realizations are cofibrations. Joint with A. Salch. arXiv

Theses

1. Phd thesis. Periodicity in iterated algebraic K-theory of finite fields

2. Masters thesis. Galois cohomology and algebraic K-theory of finite fields