Publications and Preprints
- Length of triangulated categories,
with Y. Hirano and G. Ouchi, arXiv:2404.07583v2 (pdf). - Dimension formulas for period spaces via motives and species,
with A. Huber, arXiv:2405.21053, (pdf). - Obstructions to semiorthogonal decompositions for singular projective varieties II: Representation theory,
with C. Klapproth and N. Pavic, arXiv:2404.07816, (pdf). - Cluster categories for completed infinity-gons I: Categorifying triangulations, with İ. Çanakçı and M. Pressland,
arXiv:2401.08378, (pdf); see also OWR 02/2024 for a summary. - A finite dimensional algebra with a phantom (a corollary of an example by J. Krah),
arXiv:2304.08417, (pdf). - Classifying dg-categories of matrix factorizations,
arXiv:2108.03292, (pdf). - A new equivalence between singularity categories of commutative algebras,
Advances in Mathematics, Volume 390 (2021), 107913, (pdf). - Obstructions to semiorthogonal decompositions for singular threefolds I: K-theory, with N. Pavic and E. Shinder,
Moscow Mathematical Journal, vol. 21, issue 3, 567--592 (2021), (pdf). - Relative singularity categories III: : Cluster resolutions, with D. Yang,
arXiv:2006.09733, (pdf). - Relative singularity categories II: dg-models, with D. Yang,
arXiv:1803.08192, (pdf). -
Ringel duality for certain strongly quasi-hereditary algebras, with J. Karmazyn,
European Journal of Mathematics 4 (2018), 1100--1140,
Special volume dedicated to the memory of William Edge, (pdf). -
Noncommutative Knörrer type equivalences via noncommutative resolutions of singularities, with J. Karmazyn,
arXiv:1707.02836, (pdf). -
Derived categories of graded gentle one-cycle algebras, with D. Yang,
Journal of Pure and Applied Algebra, Volume 222, Issue 10, (2018), 3005--3035, (pdf). - Derived categories of quasi-hereditary algebras and their derived composition series,
In Representation theory - current trends and perspectives, EMS Ser. Congr. Rep., 269--308. Eur. Math. Soc., Zürich, 2017, (pdf). - Spherical subcategories in representation theory, with A. Hochenegger and D. Ploog,
Mathematische Zeitschrift 291 (1-2): 113--147, 2019, (pdf). - Frobenius categories, Gorenstein algebras and rational surface singularities,
with O. Iyama, M. Wemyss and D. Yang,
Compositio Mathematica, vol. 151, issue 03, 502--534 (2015), (pdf). - Spherical subcategories in algebraic geometry, with A. Hochenegger and D. Ploog,
Mathematische Nachrichten, 289 (2016) 1450--1465, (pdf). - Singularity categories of gentle algebras,
Bulletin of the London Mathematical Society 47 (2015) 65--74, (pdf). - Relative singularity categories I: Auslander resolutions, with D. Yang,
Advances in Mathematics, vol. 301, 973--1021 (2016), (pdf). - The relative singularity category of a non-commutative resolution of singularities, with I. Burban,
Advances in Mathematics, vol. 231, no. 1, 414--435 (2012), (pdf).
Conference Proceedings:
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Derived categories of singular varieties and finite dimensional algebras,
in Oberwolfach Report 07/2023, Representation Theory of Quivers and Finite-Dimensional Algebras (pdf).
(Based on upcoming joint works with Y.Kawamata & N.Pavic and C. Klapproth & N. Pavic)
On equivalences between singularity categories of commutative rings,
in Oberwolfach Report 06/2023, Resolutions in Local Algebra and Singularity Theory (pdf).
(Based on articles 14. and 15. above.)
On Leclerc's Frobenius categories,
In proceedings of the CRM-workshop Homological Bonds between Commutative Algebra and Representation Theory
in Research Perspectives CRM Barcelona , Spring 2015, vol. 5, Trends in Mathematics, Springer-Birkhäuser, (pdf).
Relative singularity categories,
in Oberwolfach Report 44/2013, Matrix Factorizations in Algebra, Geometry, and Physics (pdf).
(Based on articles 2. and 5. above.)
Theses:
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Relative singularity categories, PhD Thesis, Bonn 2013, (pdf).
Verallgemeinerungen präprojektiver Algebren, Diploma Thesis (in German), Bonn 2009.