Research

Papers

  1. On the Infinite Loop Spaces of Algebraic Cobordism and Motivic Sphere (with Tom Bachmann, Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 40 pages, 11 pages). [Arxiv:1911] (preliminary version, comments welcome, last updated November 6 2019)
  2. Modules over Algebraic Cobordism (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 40 pages). [Arxiv:1908] (preliminary version, comments welcome, last updated August 7 2019).
  3. Perfection in Motivic Homotopy Theory. (with Adeel Khan, 10 pages). Proc. London. Math. Soc. 120 (2019), 28-38 [Arxiv:1812][PLMS].
  4. Relative Étale Realizations of Motivic Spaces and Dwyer-Friedlander K-theory of noncommutative schemes. (with David Carchedi, 81 pages) [Arxiv:1810] (preliminary version, comments welcome, last updated October 12 2018).
  5. Frames Transfers and Motivic Fundamental Classes. (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 39 pages) [Arxiv:1809] to appear in J. Topol.
  6. Thesis: Motivic Contractibility of the Space of Rational Maps (preliminary version, comments welcome, last updated April 28 2018) (To be split into two papers).
  7. Algebraic Cobordism and Étale Cohomology (with Marc Levine, Markus Spitzweck and Paul Arne Østvær). [Arxiv:1711] (submitted, comments welcome, last updated Feb 7 2019).
  8. Motivic Infinite Loop Spaces (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson[Arxiv:1711] (submitted, last updated: May 21 2018).
  9. On Modules over Motivic Ring Spectra (with Håkon Andreas Kolderup) [Arxiv:1708.05651] to appear in Ann. K-Theory.
  10. 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].
  11. Some nontrivial examples of the BOS twisted spectral sequence (with Igor Kriz). New York J. Math. 22 (2016) 363–378. [Arxiv:1604] [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 Ktheory 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. Étale Descent for Semiorthogonal Decompositions (with Benjamin Antieau).
  7. Genuine Stabilization of G-Topoi and Motivic Homotopy Theory (with Jay Shah)
  8. K-theory of Universal Homeomorphisms (with Akhil Mathew and Jakub Witaszek)
  9. The Universal Property of Bispans I & II (with Rune Haugseng)
  10. Excision and descent in Motivic Homotopy Theory (with Marc Hoyois, Ryomei Iwasa and Shane Kelly)