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Research

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

Published papers

  • Journal of Pure and Applied Algebra A homological approach to chromatic complexity of algebraic K-theory. Joint with J.D. Quigley. Publication

  • 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

  • Real syntomic cohomology. Joint with Hana Jia Kong and J.D. Quigley. arXiv

  • 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

Preprints in progress

  • Spoke topological Hochschild homology and the Segal conjecture. Joint with Foling Zou. Current draft 18 pages.

  • Syntomic cohomology of truncated Brown-Peterson spectra. Joint with J. Hahn and D. Wilson. Current draft 17 pages.

  • A C_3-equivariant Snaith construction. Joint with M. Behrens, E. Belmont, H. J. Kong, and M. Johnson. Current draft 51 pages.

  • Syntomic cohomology of topological modular forms. Joint with Ch. Ausoni, R.R. Bruner, J.M. Davies, J. Rognes, and T. Yang. Current draft 41 pages.

Notes

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

Theses

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

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