Research

Papers and preprints:

  1. Some nontrivial examples of the BOS twisted spectral sequence (with Igor Kriz). New York J. Math. 22 (2016) 363–378. [Arxiv:1604] [NYJM].
  2. 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].
  3. On modules over motivic ring spectra (with Håkon Andreas Kolderup) Ann. K-Theory 5, 327-355 [Arxiv:1708.05651][AKT].
  4. Algebraic cobordism and étale cohomology (with Marc Levine, Markus Spitzweck and Paul Arne Østvær). [Arxiv:1711] (submitted, comments welcome, last updated Feb 2019).
  5. Motivic infinite loop spaces (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson[Arxiv:1711] (submitted, last updated: April 2020).
  6. Thesis: Motivic contractibility of the space of rational maps (preliminary version, comments welcome, last updated April 2018) (To be split into two papers).
  7. 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 2018).
  8. Framed transfers and motivic fundamental classes (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 39 pages)  Journal of Topology. 13 (2020), 460-500. [Arxiv:1809] [JTop].
  9. Perfection in motivic homotopy theory. (with Adeel Khan, 10 pages). Proc. London. Math. Soc. 120 (2019), 28-38 [Arxiv:1812][PLMS].
  10. Modules over algebraic cobordism (with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 40 pages). [Arxiv:1908] (submitted, comments welcome, last updated September 2019).
  11.  On the infinite loop spaces of algebraic cobordism and the motivic sphere (with Tom Bachmann, Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, 11 pages). [Arxiv:1911] (submitted, comments welcome, last updated March 2020).
  12. Voevodsky’s slice conjectures via Hilbert schemes (with Tom Bachmann, 8 pages) [Arxiv:1912] (submitted, comments welcome, last updated December 2019).
  13. Descent for semiorthogonal decompositions (with Benjamin Antieau, 30 pages) [Arxiv:1912] (submitted, comments welcome, last updated December 2019).
  14. Scheiderer motives and equivariant higher topos theory (with Jay Shah, 78 pages). [Arxiv:1912] (submitted, comments welcome, last updated December 2019).
  15. Cdh descent, cdarc descent and Milnor excision (with Marc Hoyois, Ryomei Iwasa and Shane Kelly, 27 pages) [Arxiv:2002] (accepted, pending revision at Math. Ann.).
  16. Stable motivic invariants are eventually étale local  (with Tom Bachmann and Paul Arne Østvær, 32 pages) [Arxiv:2003] (submitted, comments welcome, last updated March 2020).
  17. Milnor excision for motivic spectra (with Marc Hoyois, Ryomei Iwasa and Shane Kelly, 9 pages) [Arxiv:2004(submitted, comments welcome, last updated, April 2020)
  18. THH and TC are (very) far from being homotopy functors (10 pages) [Arxiv:2007] (preliminary version, comments welcome, last updated July 2020).
  19. A descent view on Mitchell’s theorem (with Denis Nardin and Lucy Yang, 5 pages) (preliminary version, comments welcome, last updated August 2020).

Mostly expository:

  1. Notes on motivic infinite loop space theory (with Tom Bachmann). [Arxiv:1912].
  2. Topological periodic cyclic homology of smooth \mathbb{F}_p-algebras. (After Bhatt-Morrow-Scholze) (MFO report, last updated May 2018).

In Preparation:

  1. Nilpotent extensions of weighted \infty-categories and a multi-object Dundas-Goodwillie-McCarthy theorem (with Vladimir Sosnilo).
  2. Excision for Brauer stacks.
  3. Gabber-Suslin rigidity for iterated K-theory (with Tomer Schlank).
  4. Twisted homotopy K-theory and twisted cycle class maps.
  5. Étale framed motives (now part of the thesis of Ola Sande, co-supervised with Paul Arne Østvær).
  6. Mod 2 Power operations on normed motivic spectra (with Tom Bachmann and Jeremiah Heller).
  7. K-theory of universal homeomorphisms (with Akhil Mathew and Jakub Witaszek). (slides) (video).
  8. The universal property of bispans I & II (with Rune Haugseng).
  9. Something about continuous invariants of analytic spaces (with Martin Speirs and Yifei Zhao).