Liran Shaul

I am an assistant professor (tenure-track) at the Department of Algebra at Charles University in Prague.

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

Contact

Email: shaul at karlin.mff.cuni.cz

Derived categories conference in Prague, February 2020

Publications

  1. Gorenstein symmetry and acyclic complexes of injectives. 2023. Preprint.
  2. Categorical properties of reduction functors over non-positive DG-rings. 2022. Submitted.
  3. The finitistic dimension conjecture via DG-rings. 2022. Submitted.
  4. Finitistic dimensions over commutative DG-rings. With Isaac Bird, Prashanth Sridhar and Jordan Williamson. 2022. Submitted.
  5. Sequence-regular commutative DG-rings. 2021. Submitted.
  6. Lifting (co)stratifications between tensor triangulated categories. With Jordan Williamson. To appear in Israel Journal of Mathematics (2022).
  7. Open loci results for commutative DG-rings. Journal of Pure and Applied Algebra 226 (2022), no. 5, Paper No. 106922.
  8. Koszul complexes over Cohen-Macaulay rings. Advances in Mathematics, Volume 386, 6 August 2021.
  9. Smooth flat maps over commutative DG-rings. Mathematische Zeitschrift (2021) 299:1673–1688
  10.  Pole placement for overdetermined 2D systems. With Victor Vinnikov. Linear Algebra and Its Applications 610 (2021) pp. 529-559.
  11. The Cohen-Macaulay property in derived commutative algebra. Transactions of the AMS 373 (2020), no. 9, 6095–6138.
  12.  Completion and torsion over commutative DG rings. Israel Journal of Mathematics, , Volume 232, Issue 2, pages 531–588.
  13.  Injective DG-modules over non-positive DG-rings. Journal of Algebra 515 (2018) pp. 102-156
  14. Homological dimensions of local (co)homology over commutative DG-rings. Canadian Mathematical Bulletin 61(2018), no. 4, 865-877
  15. Tensor product of dualizing complexes over a field. J. Commut. Algebra, Volume 10, Number 2 (2018), 243-263.
  16. 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.
  17.  The twisted inverse image pseudofunctor over commutative DG rings and perfect base change.  Advances in Mathematics, Volume 320, 7 November 2017, Pages 279-328.
  18. Hochschild cohomology commutes with adic completion. Algebra & Number Theory 10-5 (2016), 1001-1029.
  19. Relations between derived Hochschild functors via twisting. Communications in Algebra 44:7 (2016), 2898-2907.
  20. Reduction of Hochschild cohomology over algebras finite over their center. Journal of Pure and Applied Algebra 219 (2015), 4368-4377.
  21. Cohomologically Cofinite Complexes. With Marco Porta and Amnon Yekutieli. Communications in Algebra Volume 43, Issue 2, 2015.
  22. 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.
  23. 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

2022/2023 spring semester

  1. Commutative algebra.

2022/2023 winter semester

  1. Categories of modules and homological algebra.
  2. Algebraic Geometry.

2021/2022 spring semester

  1. Commutative algebra.
  2. Algebra 2 for computer science.

2021/2022 winter semester

  1. Categories of modules and homological algebra.
  2. Algebraic Geometry.

2020/2021 spring semester

  1. Categories of modules and homological algebra.
  2. Algebra 2 for computer science.

2020/2021 winter semester

  1. Algebraic Geometry.
  2. Algebra I.

2019/2020 spring semester

  1. Categories of modules and homological algebra.
  2. Algebra 2 for computer science.

2019/2020 winter semester

  1. Algebraic Geometry.
  2. Algebra I.

2018/2019 spring semester

  1. Categories of modules and homological algebra.
  2. Algebra 2 for computer science.

2018/2019 winter semester

  1. Derived categories and their applications in commutative algebra.
  2. Algebraic Geometry.

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.