# Research

Papers

1. Relative Étale Realizations of Motivic Spaces and Dwyer-Friedlander $K$-theory of noncommutative schemes. (with David Carchedi, 81 pages) [Arxiv:1810.05544] (preliminary version, comments welcome, last updated October 12 2018).
2. Framed Transfers and Motivic Fundamental Classes (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 39 pages) [Arxiv:1809:10666] (preliminary version, comments welcome, last updated September 28 2018).
3. Thesis: Motivic Contractibility of the Space of Rational Maps (preliminary version, comments welcome, last updated April 28 2018) (To be split into two papers).
4. Motivic Landewber Exact Theories and Étale Cohomology (with Marc Levine, Markus Spitzweck and Paul Arne Østvær). [Arxiv:1711:06258] (preliminary version, comments welcome, last updated Nov 16 2017).
5. Motivic Infinite Loop Spaces (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson[Arxiv:1711:05248] (submitted, last updated: May 21 2018).
6. On Modules over Motivic Ring Spectra (with Håkon Andreas Kolderup) [Arxiv:1708.05651] (submitted, last updated: 28 September 2018) .
7. A Primer to Unstable Motivic Homotopy Theory (with Benjamin Antieau). Surveys on Recent Developments in Algebraic Geometry, Proc. Sympos. Pure Math. 95 (2017), 305-370. [Arxiv:1605.00929].
8. Some nontrivial examples of the BOS twisted spectral sequence (with Igor Kriz). New York J. Math. 22 (2016) 363–378. [Arxiv:1604.04260] [NYJM].

Reports

1. Topological Periodic Cyclic Homology of Smooth $\mathbb{F}_p$-algebras. (After Bhatt-Morrow-Scholze) (submitted, Oberwolfach Report, last updated May 26 2018).

In Preparation

1. Twisted Homotopy $K$theory and Twisted Cycle Class Maps.
2. Étale Framed Motives.
3. A Kahn-Priddy Theorem in Motivic Homotopy Theory (with Maria Yakerson).
4. Mod 2 Power Operations in Normed Motivic Spectra (with Tom Bachmann and Jeremiah Heller).
5. Inverting the Spherical Bott element (with Tom Bachmann and Paul Arne Østvær).
6. Perfection in Motivic Homotopy Theory (with Adeel Khan).