I work primarily in the areas of homotopy theory and $\infty$-category theory, with the focus on studying cohomology theories of geometric objects, such as algebraic varieties
Publications and preprints
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Pretriangulated categories failing (TR4). preprint
joint with Xiao-Wu Chen, Sergei O. Ivanov, Jian Liu, Xue-Song Lu and Chencheng Zhang -
Dualizable additive categories. preprint
joint with Ishan Levy and Jiacheng Liang -
$c$-structures and trace methods beyond connective rings. preprint
joint with Ishan Levy -
Every motive is the motive of a stable $\infty$-category. Journal of the European Mathematical Society, to appear
joint with Maxime Ramzi and Christoph Winges -
On filtered algebraic K-theory of stacks I: characteristic zero. preprint
joint with Elden Elmanto and Dmitry Kubrak -
Every spectrum is the K-theory of a stable $\infty$-category. preprint
joint with Maxime Ramzi and Christoph Winges -
Categorical Milnor squares and K-theory of algebraic stacks. Selecta Mathematica, 28 (2022)
joint with Tom Bachmann, Adeel A. Khan and Charanya RaviWarning: Lemma 3.5.5 contains a gap
This means that currently we can only show that the squares appearing in Theorems A, B and C are weakly cartesian and not cartesian. In Theorem 3.5.11 we have to assume that the localizing invariant is connected in the sense of Land-Tamme. The statements for connected invariants and the proofs that do not rely on this lemma can be found in my thesis
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Zariski-local framed $\mathbb{A}^1$-homotopy theory. Algebraic & Geometric Topology, to appear
joint with Andrei Druzhinin