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

**Publications**

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

- 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 - Towards coherent duality over derived formal schemes – “Hochschild Cohomology in Algebra, Geometry, and Topology”, 2016,
**Oberwolfach reports**. - 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**

2021/2022 spring semester

- Commutative algebra.
- Algebra 2 for computer science.

2021/2022 winter semester

- Categories of modules and homological algebra.
- Algebraic Geometry.

2020/2021 spring semester

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

2020/2021 winter semester

- Algebraic Geometry.
- Algebra I.

2019/2020 spring semester

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

2019/2020 winter semester

- Algebraic Geometry.
- Algebra I.

2018/2019 spring semester

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

2018/2019 winter semester

- Derived categories and their applications in commutative algebra.
- 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.