Research

My research is in motivic homotopy theory, which is a diverse mixture of algebraic geometry,

homotopy theory and algebraic K-theory.

Recently, I became interested in enumerative geometry and its interactions with homotopy theory.

Preprints

• Twisted K-theory in motivic homotopy theory (with Elden Elmanto and Denis Nardin)
• Hermitian K-theory via oriented Gorenstein algebras (with Marc Hoyois, Joachim Jelisiejew and Denis Nardin)
  
  

Papers

• The Hilbert scheme of infinite affine space and algebraic K-theory (with Marc Hoyois, Joachim Jelisiejew, Denis Nardin and
  Burt Totaro)
  to appear in the Journal of the European Mathematical Society 
• Motivic infinite loop spaces (with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo)
  Cambridge Journal of Mathematics, 9-2 (2021), 431–549. 
• On the infinite loop spaces of algebraic cobordism and the motivic sphere (with Tom Bachmann, Elden Elmanto, Marc Hoyois,
  Adeel Khan and Vladimir Sosnilo) 
  Épijournal Géom. Algébrique 5 (2021), Article Nr. 9. 
• Modules over algebraic cobordism (with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo)
  Forum of Mathematics, Pi, 8-e14 (2020), 1-44. 
• Towards conservativity of Gm-stabilization  (with Tom Bachmann)
  Journal of Geometry & Topology 24-4 (2020), 1969-2034.
• Framed transfers and motivic fundamental classes (with Elden Elmanto, Marc Hoyois, Adeel Khan and Vladimir Sosnilo)
  Journal of Topology 13 (2020), 460–500.
• The unit map of the algebraic special linear cobordism spectrum
  Journal of the Institute of Mathematics of Jussieu (2019), 1-26, published online
• Algebraic K-theory of varieties SL2n / Sp2n,  E6 / F4 and their twisted forms
  Algebra and Analysis 28 (2016), no. 3, 174-189, in Russian. Translation: St. Petersburg Mathematical Journal 28 (2017), no. 3,  421-431.

Other

• Motivic stable homotopy groups via framed correspodences. PhD thesis, Duisburg-Essen University.
• Higher Chow-Witt groups. Oberwolfach Report 29/2019, "Algebraic K-Theory".

Here are the videos of some of the talks I gave. 

• The Hilbert scheme of inifinite affine space. Algebra seminar, University of Maryland, Oct 2020
• Universality of algebraic K-theory. "Motivic geometry", Centre for Advanced Study in Oslo, Sept 2020
• Motivic generalized cohomology theories from framed perspective. Online conference "MoVid-20", April 2020
• Virtual localization formula of Graber-Pandharipande. Motives seminar in Essen, December 2020