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I’m an associate professor at the Centre for Quantum Mathematics (QM) at Syddansk Universitet in Odense, Denmark.

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

News

Preprint. My PhD student Charalampos (Harry) Evangelatos and I have uploaded our paper Gluing abelian categories and stability conditions to the arxiv. We revisit the gluing of stability conditions along semiorthogonal decompositions, giving a concrete description of the heart and identifying general conditions under which the support property holds.

Award. Ludmil Katzarkov, Maxim Kontsevich, and I received an ICBS 2026 Frontiers of Science Award for the paper Flat surfaces and stability structures (published in Publ. Math. IHES in 2017). I feel incredibly honored by this recognition of our work.

Funding. I am one of several inaugural recipients of a Villum Ascending Investigator grant from the Villum Foundation for my project The Quantum Geometry of Dynamical Systems. The grant will support three PhD students and three postdocs over the next five years. I am very grateful for the Foundation’s support of fundamental research in the natural and technical sciences.

Papers and preprints

  1. Gluing abelian categories and stability conditions (with C. Evangelatos), arxiv:2608.21201
  2. A counterexample to the Jordan-Hölder property for polarizable semiorthogonal decompositions (with D. Wu), arxiv:2502.12075
  3. The stability manifold of E x E x E (with B. Sung), arxiv:2410.08028,
  4. Counting in Calabi-Yau categories, with applications to Hall algebras and knot polynomials (with M. Gorsky), arxiv:2409.10154
  5. Perverse schobers, stability conditions and quadratic differentials II: Relative graded Brauer graph algebras (with M. Christ, Y. Qiu), Selecta Math. 32:62, 2026, arxiv:2407.00154, journal
  6. Perverse schobers, stability conditions and quadratic differentials I (with M. Christ, Y. Qiu), to appear in Compositio Math., arXiv:2303.18249
  7. Braid group actions on branched coverings and full exceptional sequences (with W. Chang, S. Schroll), Adv. Math. 472, 110284, 2025, arXiv:2301.04398, journal
  8. Spectral networks and stability conditions for Fukaya categories with coefficients (with L. Katzarkov, C. Simpson), Commun. Math. Phys. 405:264, 2024, arXiv:2112.13623, journal
  9. 3-d Calabi-Yau categories for Teichmüller theory, Duke Math. J. 173 (2), p. 277–346, 2024. arXiv:2104.06018
  10. On pseudo-Anosov autoequivalences (with Y.-W. Fan, S. Filip, L. Katzarkov, Y. Liu), Adv. Math. 384, 2021. arXiv:1910.12350
  11. Flags and Tangles, Quantum Topology 12, p. 461-505, 2021. arXiv:1910.04182
  12. Legendrian skein algebras and Hall algebras, Math. Ann., 2021. arXiv:1908.10358
  13. 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
  14. Iterated logarithms and gradient flows (with P. Pandit, L. Katzarkov, M. Kontsevich), arxiv:1802.04123
  15. 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
  16. Flat surfaces and stability structures (with L. Katzarkov, M. Kontsevich), Publ. Math. IHES 126, p. 247–318, 2017. arxiv:1409.8611
  17. 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
  18. 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
  19. Stability of 1-dimensional A-branes (PhD thesis), 2015, Uni Wien
  20. 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.

Current teaching (fall ’26)

MM554: Mathematics for Biology, MM556: Mathematics and Statistics for Pharmacy

Collaborators

Wen Chang, Merlin Christ, George Dimitrov, Charalampos Evangelatos, Yu-Wei Fan, David Favero, Simion Filip, Mikhail Gorsky, Ludmil Katzarkov, Maxim Kontsevich, Yijia Liu, Pranav Pandit, Yu Qiu, Sibylle Schroll, Carlos Simpson, Benjamin Sung, Dongjian Wu