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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: [email protected]

preprints on the arXiv | Google scholar profile

News

New preprint! “A counterexample to the Jordan-Hölder property for polarizable semiorthogonal decompositions” with Dongjian Wu. We show that the Jordan-Hölder property fails for polarizable semiorthogonal decompositions – those where every factor admits a Bridgeland stability condition. Counterexamples exist among Fukaya categories of surfaces and bounded derived categories of smooth projective varieties. Furthermore, we give an example of a smooth and proper pre-triangulated dg category with positive rank Grothendieck group which does not admit a stability condition.

New preprint! “The stability manifold of E x E x E” with Ben Sung. It is typically a challenging problem to determine a full component of the space of stability conditions on a triangulated category. We solve this problem for the derived category of coherent sheaves on the cube of an elliptic curve without complex multiplication, confirming an expectation of Kontsevich motivated by mirror symmetry.

New preprint! “Counting in Calabi-Yau categories, with applications to Hall algebras and knot polynomials” with Mikhail Gorsky. We solve a long-standing open problem in the theory of Hall algebras (defining it intrinsically) in the case of Calabi-Yau categories of odd dimension. The second main result relates certain knot polynomials to homotopy cardinality of dg-categories, proving a conjecture of Ng-Rutherford-Shende-Sivek. A video recording of my talk on this at Kontsevich’s 60th birthday conference can be found here.

Lecture series. I am giving an introductory mini-course on stability conditions as part of the Simons Center program Geometric, Algebraic, and Physical structures around the moduli of Meromorphic Quadratic Differentials. Lecture notes can be found here. Videos available here.

Papers and preprints

  1. A counterexample to the Jordan-Hölder property for polarizable semiorthogonal decompositions (with D. Wu), arxiv:2502.12075
  2. The stability manifold of E x E x E (with B. Sung), arxiv:2410.08028
  3. Counting in Calabi-Yau categories, with applications to Hall algebras and knot polynomials (with M. Gorsky), arxiv:2409.10154
  4. Perverse schobers, stability conditions and quadratic differentials II: Relative graded Brauer graph algebras (with M. Christ, Y. Qiu), arxiv:2407.00154
  5. Perverse schobers, stability conditions and quadratic differentials I (with M. Christ, Y. Qiu), arXiv:2303.18249
  6. Braid group actions on branched coverings and full exceptional sequences (with W. Chang, S. Schroll), Adv. Math. 472, 110284, 2025, arXiv:2301.04398, journal
  7. 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
  8. 3-d Calabi-Yau categories for Teichmüller theory, Duke Math. J. 173 (2), p. 277–346, 2024. arXiv:2104.06018
  9. On pseudo-Anosov autoequivalences (with Y.-W. Fan, S. Filip, L. Katzarkov, Y. Liu), Adv. Math. 384, 2021. arXiv:1910.12350
  10. Flags and Tangles, Quantum Topology 12, p. 461-505, 2021. arXiv:1910.04182
  11. Legendrian skein algebras and Hall algebras, Math. Ann., 2021. arXiv:1908.10358
  12. 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
  13. Iterated logarithms and gradient flows (with P. Pandit, L. Katzarkov, M. Kontsevich), arxiv:1802.04123
  14. 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
  15. Flat surfaces and stability structures (with L. Katzarkov, M. Kontsevich), Publ. Math. IHES 126, p. 247–318, 2017. arxiv:1409.8611
  16. 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
  17. 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
  18. Stability of 1-dimensional A-branes (PhD thesis), 2015, Uni Wien
  19. 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 ’25)

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

Collaborators

Wen Chang, Merlin Christ, George Dimitrov, 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