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I’m an assistant professor at the Centre for Quantum Mathematics at Syddansk Universitet.

I study interactions between geometry, dynamics, and category theory. See the research page for more details on my current projects. The best way to get in touch is by email: fab@sdu.dk

preprints on the arXiv | Google scholar profile | CV

News

New preprint with Merlin Christ and Yu Qiu: Perverse schobers, stability conditions and quadratic differentials (arXiv:2303.18249). This unifies and generalizes many of the previous works on quadratic differentials and stability conditions using Fukaya categories of surfaces with coefficients in perverse schobers. Novel examples include relative and graded variants of Brauer graph algebras.

New preprint with Wen Chang and Sibylle Schroll: Braid group actions on branched coverings and full exceptional sequences (arXiv:2301.04398). We show a correspondence between branched coverings and full exceptional collections in Fukaya categories of surfaces. As an application, we find examples where the action of the braid group on full exceptional collections is not transitive, contradicting a long-standing conjecture.

Papers and preprints

  1. Perverse schobers, stability conditions and quadratic differentials (with M. Christ, Y. Qiu), arXiv:2303.18249
  2. Braid group actions on branched coverings and full exceptional sequences (with W. Chang, S. Schroll), arXiv:2301.04398
  3. Spectral networks and stability conditions for Fukaya categories with coefficients (with L. Katzarkov, C. Simpson), arXiv:2112.13623
  4. 3-d Calabi-Yau categories for Teichmüller theory, to appear in Duke Math. J., arXiv:2104.06018
  5. On pseudo-Anosov autoequivalences (with Y.-W. Fan, S. Filip, L. Katzarkov, Y. Liu), Adv. Math. 384, 2021. arXiv:1910.12350
  6. Flags and Tangles, to appear in Quantum Topology, arXiv:1910.04182
  7. Legendrian skein algebras and Hall algebras, Math. Ann., 2021. arXiv:1908.10358
  8. An extension of the Siegel space of complex abelian varieties and conjectures on stability structures, manuscripta math. 163, p. 87–111, 2020. arxiv:1808.06364
  9. Iterated logarithms and gradient flows (with P. Pandit, L. Katzarkov, M. Kontsevich), arxiv:1802.04123
  10. Semistability, modular lattices, and iterated logarithms (with P. Pandit, L. Katzarkov, M. Kontsevich), J. Differential Geom. 123 (1), p. 21–66, 2023, arxiv:1706.01073
  11. Flat surfaces and stability structures (with L. Katzarkov, M. Kontsevich), Publ. Math. IHES 126, p. 247–318, 2017. arxiv:1409.8611
  12. Dynamical systems and categories (with G. Dimitrov, L. Katzarkov, M. Kontsevich), in The Influence of Solomon Lefschetz in Geometry and Topology: 50 Years of Mathematics at CINVESTAV, Con. Math. 621, p. 133–170, 2014. arxiv:1307.8418
  13. An Orbit Construction of Phantoms, Orlov Spectra, and Knörrer Periodicity (with D. Favero, L. Katzarkov), in Homological Mirror Symmetry and Tropical Geometry, Lecture Notes of the Unione Matematica Italiana 15, p. 33–42, 2014. Springer
  14. Stability of 1-dimensional A-branes (PhD thesis), 2015, Uni Wien
  15. Refined Combinatorial Torsion (MSc thesis), 2010, Uni Wien

Events

I’m co-organizing the QM Research Seminar – upcoming talks

29th Nordic Congress of Mathematicians (3-7 July 2023, Aalborg, Denmark). I’m co-organizing the special session The ubiquity of quivers and their representations with Bernhard Keller and Vidit Nanda.

Collaborators