Liran Shaul

I am an associate professor at the Department of Algebra at Charles University in Prague.

Contact

Email: shaul at karlin.mff.cuni.cz

Derived categories conference in Prague, February 2020

Publications

  1. Formalization in Lean of faithfully flat descent of projectivity. Code. 2026, Submitted.
  2. Openness with respect to levels in triangulated categories. With Souvik Dey and Jian Liu. 2025. Submitted.
  3. “Differential graded rings and their applications” – Habilitation thesis. Approved, 2025.
  4. Gorenstein acyclic complexes and finitistic dimensions. 2023. Submitted.
  5. Acyclic complexes of injectives and finitistic dimensions. With an appendix by Tsutomu Nakamura and Peder Thompson. 2023. Submitted.
  6. Categorical properties of reduction functors over non-positive DG-rings. Proceedings of the AMS 152 (2024), 489-500.
  7. The finitistic dimension conjecture via DG-rings. 2022. Submitted.
  8. Finitistic dimensions over commutative DG-rings. With Isaac Bird, Prashanth Sridhar and Jordan Williamson. Mathematische Zeitschrift (2025) 309, no.1, Paper No. 3.
  9. Sequence-regular commutative DG-rings. Journal of Algebra 647, 1 June 2024, Pages 400-435(2024).
  10. Lifting (co)stratifications between tensor triangulated categories. With Jordan Williamson. Israel Journal of Mathematics Volume 261, pages 249–280, (2024).
  11. Open loci results for commutative DG-rings. Journal of Pure and Applied Algebra 226 (2022), no. 5, Paper No. 106922.
  12. Koszul complexes over Cohen-Macaulay rings. Advances in Mathematics, Volume 386, 6 August 2021.
  13. Smooth flat maps over commutative DG-rings. Mathematische Zeitschrift (2021) 299:1673–1688
  14.  Pole placement for overdetermined 2D systems. With Victor Vinnikov. Linear Algebra and Its Applications 610 (2021) pp. 529-559.
  15. The Cohen-Macaulay property in derived commutative algebra. Transactions of the AMS 373 (2020), no. 9, 6095–6138.
  16.  Completion and torsion over commutative DG rings. Israel Journal of Mathematics, , Volume 232, Issue 2, pages 531–588.
  17.  Injective DG-modules over non-positive DG-rings. Journal of Algebra 515 (2018) pp. 102-156
  18. Homological dimensions of local (co)homology over commutative DG-rings. Canadian Mathematical Bulletin 61(2018), no. 4, 865-877
  19. Tensor product of dualizing complexes over a field. J. Commut. Algebra, Volume 10, Number 2 (2018), 243-263.
  20. Adic reduction to the diagonal and a relation between cofiniteness and derived completion. Proceedings of the AMS, Volume 145, Number 12, December 2017, Pages 5131-5143.
  21.  The twisted inverse image pseudofunctor over commutative DG rings and perfect base change.  Advances in Mathematics, Volume 320, 7 November 2017, Pages 279-328.
  22. Hochschild cohomology commutes with adic completion. Algebra & Number Theory 10-5 (2016), 1001-1029.
  23. Relations between derived Hochschild functors via twisting. Communications in Algebra 44:7 (2016), 2898-2907.
  24. Reduction of Hochschild cohomology over algebras finite over their center. Journal of Pure and Applied Algebra 219 (2015), 4368-4377.
  25. Cohomologically Cofinite Complexes. With Marco Porta and Amnon Yekutieli. Communications in Algebra Volume 43, Issue 2, 2015.
  26. On the Homology of Completion and Torsion. With Marco Porta and Amnon Yekutieli. Algebras and Representation Theory February 2014, Volume 17, Issue 1, pp 31-67. Errata.
  27. Completion by Derived Double Centralizer. With Marco Porta and Amnon Yekutieli. Algebras and Representation Theory April 2014, Volume 17, Issue 2, pp 481-494.

Conference proceedings

  1. Tensor product of dualizing complexes over a field. In: Herbera D., Pitsch W., Zarzuela S. (eds) Extended Abstracts Spring 2015. Trends in Mathematics, vol 5. Birkhäuser, Cham
  2. Towards coherent duality over derived formal schemes – “Hochschild Cohomology in Algebra, Geometry, and Topology”, 2016, Oberwolfach reports.
  3. State feedback for overdetermined 2D systems: pole placement for bundle maps over an algebraic curve. With Victor Vinnikov. International Workshop on Multidimensional (nD) Systems, IEEE, 2009

Teaching

In the 2025/2026 winter semester I teach a course on Homological algebra and a course on Algebraic Geometry.

Grants

I was the principal investigator of the grant “Cohen-Macaulay rings and their applications in higher algebra and topology“.

Student supervision

PhD students

  1. Jindřich Novák (since October 2025).

Master students supervised

  1. Enrico Sabatini (graduated 2022, joint supervision with Prof. Jorge Nuno Dos Santos Vitória).
  2. Jindřich Novák (graduated 2025).
  3. Alžběta Kocmanová (since October 2025).

Bachelor thesis supervised

  1. Edward Young (graduated 2023).
  2. Emil Čuřín (graduated 2024).

Conferences

In Februrary 2020 I organized the conference Derived Categories.

Past positions

Before coming to Prague, I was a postdoctoral researcher at Bielefeld, Germany, hosted by Prof. Henning Krause, at Antwerp, Belgium, hosted by Prof. Wendy Lowen, at the Weizmann institute, Israel, and at Ben-Gurion university of the Negev. I graduated from Ben-Gurion at 2013. My PhD advisor was Prof. Amnon Yekutieli.