Amit Shah

About me

I have been selected to be a member of the European Mathematical Society Young Academy (EMYA), which promotes and supports early-career mathematicians across Europe. I was elected to be a member of the EMYA Committee in Oct 2024.

From Mar 2021 to Dec 2024, I was a postdoc in the Aarhus Homological Algebra Group at Aarhus University, Denmark. I organised the seminar series between Fall 2023 and Fall 2024.

Before this: I was an LMS Early Career Fellow with support from Heilbronn (Dec 2020–Feb 2021) at University of Leeds. I was a postdoc (Nov 2019–Nov 2020) at Newcastle University as part of the Higher Dimensional Homological Algebra project. I completed my PhD, titled Partial cluster-tilted algebras via twin cotorsion pairs, quasi-abelian categories and Auslander-Reiten theory, under the supervision of  Prof. Bethany R. Marsh at University of Leeds in 2019.

CV

My CV can be found here.

Research interests

Classical & Higher homological algebra; Representation theory of algebras; Category theory, including triangulated, exact and non-abelian categories, and their higher counterparts.

Papers/preprints 

arXiv | Google Scholar

1. Quasi-abelian hearts of twin cotorsion pairs on triangulated categories. Journal of Algebra, 2019.

2. Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories. Journal of Pure and Applied Algebra, 2020.

3. with S. Hassoun: Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories. Communications in Algebra, 2020.

4. with R. Bennett-Tennenhaus: Transport of structure in higher homological algebra. Journal of Algebra, 2021.

5. with S. Hassoun, S.-A. Wegner: Examples and non-examples of integral categories and the admissible intersection property. Cahiers de Topologie et Géométrie Différentielle Catégoriques, 2021.

6. with P. Jørgensen: Grothendieck groups of d-exangulated categories and a modified Caldero-Chapoton map. Journal of Pure and Applied Algebra, 2024.

7. with P. Jørgensen: The index with respect to a rigid subcategory of a triangulated category. International Mathematics Research Notices, 2024.

8. with R. Bennett-Tennenhaus, J. Haugland, M. H. Sandøy: The category of extensions and a characterisation of n-exangulated functors. Mathematische Zeitschrift, 2023.

9. with C. Klapproth, D. Msapato: Idempotent completions of n-exangulated categories. Applied Categorical Structures, 2024.

10. with T. Brüstle, S. Hassoun, A. Tattar: Stratifying systems and Jordan-Hölder extriangulated categories. To appear in Glasgow Mathematical Journal, 2025.

11. Krull-Remak-Schmidt decompositions in Hom-finite additive categories. Expositiones Mathematicae, 2022.

12. with R. Bennett-Tennenhaus, J. Haugland, M. H. Sandøy: The category of extensions and idempotent completion. Theory and Applications of Categories, 2024.

13. with Y. Ogawa: A resolution theorem for extriangulated categories with applications to the index. Journal of Algebra, 2024.

14. with F. Fedele, P. Jørgensen: The index with respect to a contravariantly finite subcategory. Preprint, 2024.

15. with F. Fedele, P. Jørgensen: The index in d-exact categories. Accepted in Journal of Algebra, 2024.

16. with Y. Ogawa: Weak Waldhausen categories and a localization theorem. Preprint, 2024.

17. with R. Bennett-Tennenhaus, I. Goodbody, J. Letz: Tensor extriangulated categories. Journal of Algebra, 2026.

Organisation

• EMS Young Academy Committee (selected as internal auditor). Since Oct 2024.

• Aarhus Homological Algebra seminar series. Aarhus, Fall 2023, Spring 2024, Fall 2024.

• Masterclass of Derived Category Methods in Ring Theory. Aarhus, Aug 2024.

• Geometric & combinatorial methods in homological algebra. Aarhus, Jul 2022.

• Additive categories between algebra and functional analysis. Online, Mar 2021.

• New connections and directions in representation theory and related topics. Leeds, Apr 2019.

• Pure postgraduate seminar series. Leeds, 2017–2018.

Teaching

Aarhus University (Lectures & Problems classes, MSc supervision, Reading courses)

• • Homological Algebra (Spring 2022, 2023)

  • MSc supervision (Spring 2022, 2023)

  • Reading courses on: Representation theory of finite-dimensional algebras (Fall 2023); Derived functors and sheaf cohomology (Summer 2023)

University Teesside (Lectures & Problems classes)

• • ENG1022-N: Linear Algebra I (Fall 2020)

Newcastle University (Lectures & Problems classes)

• • MAS3707: Number Theory and Cryptography (Spring 2020)

University of Leeds (Problems classes)

• • Math 1025: Number Systems (Autumn 2015, 2016, 2017, 2018)

  • Math 1026: Sets, Sequences and Series (Spring 2016, 2017, 2018, 2019)

  • Math 1055: Numbers and Vectors (Autumn 2015)

  • Math 1060: Introductory Linear Algebra (Autumn 2018)

  • Math 1225: Introduction to Geometry (Autumn 2018)

  • Math 2027: Rings and Polynomials (Spring 2019)

University of Illinois at Chicago (Problems classes)

• Math 090: Intermediate Algebra (Fall 2013)

• Math 180: Calculus I (Fall 2014, Spring 2015)

• Math 121: Precalculus (Spring 2014)

University of Warwick (Supervisions)

• •  Real analysis, linear algebra, differential equations, geometry (2012–2013)

Notes, unpublished work, etc.

• Partial cluster-tilted algebras via twin cotorsion pairs, quasi-abelian categories and Auslander-Reiten theory (PhD thesis)

• University of Leeds 2019 PhD thesis LaTeX template

Adventures

• The Big American Paddle, 2015

• Fra Sjælland to Zealand, 2025

Contact

• Email: a.shah1728@gmail.com