Central objects in my research are so called perverse schobers, meaning categorified perverse sheaves. The general notion of perverse schobers is conjectural, but there exists a working theory for perverse schobers on surfaces with boundary.
Global sections of perverse schober describe interesting classes of stable ∞-categories and provide new local-to-global arguments for their study. There are many examples coming from Fukaya(-Seidel) categories or representation theory, the latter including the derived categories of (skew-) gentle algebras, (graded, relative) Brauer graph algebras, (relative) Ginzburg dg-algebras of triangulated surfaces and, last but not least, cluster categories of surfaces.
Perverse schobers further form natural objects of study in the emerging theory of categorified homological algebra.

Publications and preprints

  1. Relative Calabi-Yau structures and perverse schobers on surfaces
    Preprint: arXiv:2209.2311.16597.
  2. Perverse schobers, stability conditions and quadratic differentials (with Fabian Haiden and Yu Qiu)
    Preprint: arxiv:2303.18249. Submitted.
  3. Lax Addivity (with Tobias Dyckerhoff and Tashi Walde)
    Preprint: arxiv:2402.12251. Submitted. Formerly part of Complexes of stable ∞-categories.
  4. Complexes of stable ∞-categories (with Tobias Dyckerhoff and Tashi Walde)
    Preprint: arxiv:2301.02606. Submitted.
  5. Cluster theory of topological Fukaya categories
    Preprint: arXiv:2209.06595. Submitted.
  6. Geometric models for the derived categories of Ginzburg algebras of n-angulated surfaces via local-to-global principles
    Preprint: arXiv:2107.10091. Submitted.
  7. Ginzburg algebras of triangulated surfaces and perverse schobers
    Forum Math. Sigma, 10:e8, 2022, doi:10.1017/fms.2022.1. arXiv:2101.01939.
  8. Spherical monadic adjunctions of stable infinity categories
    Int. Math. Res. Not. IMRN, 2023(15):13153–13213, 2022, doi:10.1093/imrn/rnac187. arXiv:2010.05294.

Other writings