Amit Shah

About Me

NEW! I am co-organising a Masterclass of Derived Category Methods in Ring Theory and registration is open! The masterclass is aimed at PhD students and postdocs.

I have been selected to be a member of the European Mathematical Society Young Academy, which promotes and supports early-career mathematicians across Europe.

Since Mar 2021, I have been a postdoc in the Aarhus Homological Algebra Group at Aarhus University, Denmark.

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

Representation theory of algebras; tilting theory; Auslander–Reiten theory; cluster theory; classical & higher homological algebra; triangulated, exact and non-abelian categories and their higher counterparts; category theory. 

Papers/Preprints arXiv | Google Scholar

1. Quasi-abelian hearts of twin cotorsion pairs on triangulated categories. J. Algebra 534:313–338 (2019).

2. Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories. J. Pure Appl. Algebra 224(1):98–124 (2020).

3. with S. Hassoun: Integral and quasi-abelian hearts of twin cotorsion pairs on extriangulated categories. Comm. Algebra 48(12):5142–5162 (2020).

4. with R. Bennett-Tennenhaus: Transport of structure in higher homological algebra. J. Algebra 574:514–549 (2021).

5. with S. Hassoun, S.-A. Wegner: Examples and non-examples of integral categories and the admissible intersection property. Cah. Topol. Géom. Différ. Catég. LXII(3):329–354 (2021).

6. with P. Jørgensen: Grothendieck groups of d-exangulated categories and a modified Caldero-Chapoton map. J. Pure Appl. Algebra 228(5): Paper 107587 (2024).

7. with P. Jørgensen: The index with respect to a rigid subcategory of a triangulated category. Int. Math. Res. Not. IMRN 2024(4):3278–3309 (2024).

8. with R. Bennett-Tennenhaus, J. Haugland, M. H. Sandøy: The category of extensions and a characterisation of n-exangulated functors. Math. Z. 305(3): Paper 44 (2023).

9. with C. Klapproth, D. Msapato: Idempotent completions of n-exangulated categories. Appl. Categ. Structures 32: Paper 7 (2024).

10. with T. Brüstle, S. Hassoun, A. Tattar: Stratifying systems and Jordan-Hölder extriangulated categories. Preprint (2022).

11. Krull-Remak-Schmidt decompositions in Hom-finite additive categories. Expo. Math. 41(1):220–237 (2022).

12. with R. Bennett-Tennenhaus, J. Haugland, M. H. Sandøy: The category of extensions and idempotent completion. Preprint (2023).

13. with Y. Ogawa: A resolution theorem for extriangulated categories with applications to the index. Preprint (2023).

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

Teaching

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

• • Representation theory of finite-dimensional algebras reading course (Fall 2023)

  • Derived functors and sheaf cohomology reading course (Summer 2023)

  • Homological Algebra (Spring 2022, 2023)

  • MSc supervision (Spring 2022, 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

• 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

Contact

• Email: amit.shah@math.au.dk

• Mailing address: Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000 Aarhus C, Denmark