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Research

My research interests are in the areas:

  • Chromatic homotopy theory, equivariant homotopy theory and motivic homotopy theory

  • Invariants of ring spectra: algebraic K-theory, topological Hochschild homology and syntomic cohomology

Published papers

  • Advances in Mathematics A deformation of Borel equivariant homotopy. Joint with M. Behrens, E. Belmont, and H. J. Kong. Publication

  • Advances in Mathematics Real Topological Hochschild homology via the norm and Real Witt vectors. Joint with T. Gerhardt and M. A. Hill. Publication

  • 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

  • Spoke topological Hochschild homology. Joint with F. Zou. arXiv

  • 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

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

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