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Amit Shekhar Kuber
PhD (University of Manchester, UK)
Associate Professor, Department of Mathematics & Statistics
Research Interest
Representation theory of quivers, Model-theoretic K-theory of modules, Combinatorics
Department of Mathematics and Statistics, IIT Kanpur, Kalyanpur, Kanpur, Uttar Pradesh 208016
Specialization
Representation theory, Model theoretic K-theory, Combinatorics
Education
PhD (2011-14)-University of Manchester, UK
Thesis title: K-theory of theories of modules and algebraic varieties
Supervisor: Prof. Mike Prest
Master of Advanced Studies/Part-III of Mathematical Tripos (2010-11)-University of Cambridge, UK
M.Sc. (2008-10)-University of Pune
B.Sc. (2006-08)-Garware College, Pune
Teaching Area
IC courses
MTH111, MTH101: Single variable calculus ETH111: Introduction to practical ethics.
Foundations of mathematics
MTH202: Set theory and discrete mathematics, MTH302: Set theory and logic, MTH642: Topics in model theory, MTH661: Introduction to sheaves and topos theory, MTH666: Category theory.
Algebra and representation theory
MTH613: Rings and modules, MTH619: Representation theory of quivers, MTH724: Introduction to algebraic K theory.
Combinatorics
MTH678: Techniques in Combinatorics
MOOC
Set Theory and Mathematical Logic,Category Theory
Current Teaching
MTH619 Representation theory of quivers
Previous Work Experience
Assistant Professor, Department of Mathematics and Statistics, IIT Kanpur, Dec. 2016-Dec. 2022
ECI Postdoctoral Research Fellow Eduard Cech Institute for Algebra, Geometry and Physics, Czech Republic at Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic, Apr. 2016-Dec. 2016
Postdoctoral Research Fellow, Dipartimento di Matematica e Fisica, Seconda Universita degli Studi di Napoli, Caserta, Italy, Dec. 2014-Nov. 2015
Professional Affiliations
Selected Publications
On the stable radical of the module category for special biserial algebras (with Suyash Srivastava and Vinit Sinha), Journal of London Mathematical Society, 112(3) (2025), paper e70275.
Model-theoretic K1 of free modules over PIDs (with Sourayan Banerjee), Annals of Pure and Applied Logic, 176(9) (2025), paper 103613.
Hammocks for non-domestic string algebras (with Vinit Sinha, Annoy Sengupta and Bhargav Kale), Algebras and Representation Theory, 27(2024), 1869-1908.
On the order types of hammocks for domestic string algebras (with Shantanu Sardar), J. Pure Appl. Algebra, 228(12) (2024), paper 107763.
Euclidean algorithm for a class of linear orders (with Shashwat Agrawal and Esha Gupta), Discrete Mathematics, 346(12) (2023), paper 113639.
Awards & Fellowships
Gopal Das Bhandari Memorial Distinguished Teacher Award, IIT Kanpur, 3 July 2023.
Excellence-in-Teaching Award, IIT Kanpur, 5 Sept. 2022.
Sushila and Kantilal Mehta Award for motivating and encouraging students to pursue pure mathematics through teaching and research, IIT Kanpur, 28 June 2019.
Eduard Cech Institute (Czech Republic) postdoc fellowship (2016)
School of Mathematics, University of Manchester (UK) overseas students scholarship (2011-14)
Cambridge Commonwealth Trust scholarship (2010-11)
NBHM M.Sc. scholarship (2008-10)
Lt. Padmabhushan A. Garware Memorial award and Lt. R.G. Kunte Memorial award for first rank in B.Sc. (Maths) in Pune University
Conference Presentations
Linear orders, automata, word problems, and stable ranks for string algebras, ARTA X, Universität zu Köln, Germany, 1 Sept 2025
Euclidean algorithm and completeness theorem for the isomorphism problem for a class of linear orders, (Video) Calcutta Logic Circle Annual Meet, Kolkata, 9 November 2024
Hammocks for non-domestic string algebras, ARTA IX, Queen's university, Kingston, Canada, 15 June 2023
Lower algebraic K-theory, as part of K-theory in totality series organised by Grothendieck School of Thoughts, March 2023
Combinatorics of the bridge quiver and the stable rank of a string algebra, 8th virtual meeting on 'new directions in group theory and triangulated categories', 12 Jan. 2021
Categorical syntax-semantics dualities, Calcutta Logic Circle Annual Meet, Kolkata, 14 Oct. 2017
Extra Curricular Activities
Languages, Indian classical and light music: vocal, harmonium and tabla; poem writing
Keywords
Tree modules, zero-relation algebra, linear order
Research Group
Current members:
- Sourayan Banerjee (IPDF)
- Annoy Sengupta (FARE fellow)
Past members:
- Suraj Mishra (MSc, IITB)
- Mihir Mittal (BS-MS, IITK)
- Suyash Srivastava (BS, IITK) (Current: PhD at University of California Berkeley)
- Vinit Sinha (BS, IITK) (Current: PhD at Purdue University)
- Shantanu Sardar (PhD, IITK) (Current: Postdoc, CONICET, Universidad Nacional de Mar del Plata, Argentina)
- Shashwat Agrawal (BS-MS, IITK) (Current: PhD at IIT Delhi)
- Esha Gupta (BS, IITK) (Current: PhD at Université Versailles Saint-Quentin-en-Yvelines)
- Bhargav Kale (MSc, IITK) (Current: PhD at University of Arizona)
- Harshit Bisht (BS-MS, IITK) (Current: PhD, IIT Delhi)
- Arihant Jain (BS, IITK) (Current: PhD at McGill University)
- Himanshu Shukla (BT-MS, IITK) (Current: Postdoc at Bayreuth University)
Current Research
Quiver modules,
Pure-injective modules over zero-relation algebras,
Model-theoretic K1 of modules over semisimple rings
Conferences
Lead organiser, BIRS workshop "Quivers in Representation Theory", Chennai Mathematical Institute, December 2025
Co-organisers: Thomas Brüstle (Sherbrooke), Apoorva Khare (IISc), Shraddha Srivastava (IIT Dharwad).
Scientific Committee member, AESIM school "Flavours in Representation Theory" (FoRT), NEHU, July 2025
Facilitator, Maths Circle India Module 20, March-April 2025
Other facilitators: Garima Chauhan, Rohun Easwer, Mihir Mittal, Sam K Mathew
Co-organiser, NCM-funded Advanced Instructional School (AIS) "Representation Theory of Quivers and BGG Category O for semi simple Lie Algebras" (Virtual mode), December 2024
Co-organiser: Sachin Sharma
Program Committee and Organising Committee member, "Indian School on Logic and Applications (ISLA) Part-I" (Hybrid mode), IIT Kanpur, May 2022
Co-organiser: Purbita Jana
Program Committee member, Indian Conference on Logic and Applications (ICLA) (Virtual mode), 2021
Program Committee Chair, Indian School on Logic and Applications (ISLA) 2020 (Virtual mode), Dec. 2020
Program Committee member, Indian Conference on Logic and Applications (ICLA), IIT Delhi, 2019
UG/PG Courses Developed
MTH619: Representation theory of quivers
MTH642: Topics in model theory
MTH661: Introduction to sheaves and topos theory
MTH666: Category theory
MTH678A: Techniques in combinatorics
MTH724: An introduction to algebraic K-theory
Academic Positions
Dame Kathleen Ollerenshaw Visiting Professor, Department of Mathematics, University of Manchester, UK, Oct. 2019
Administrative posts held in academic organizations
Board of Studies, MES Abasaheb Garware College, Pune, 2022-present
- Member of the Association for Symbolic Logic (ASL) committee on Membership, 2021-2023
Executive Committee member of the Association for Logic in India (ALI)-2019-2021, 2021-2023
Invited Lectures
Kyu Padhe Bhai? Joy of rigour in calculus, SciMathSoc, IITK, 10 Sept. 2025
Quivers: a combinatorial approach to representation theory, NEHU, Shillong, 13 November 2024
Maths in melody, Stamatics, IITK, 5 March 2024
From Hilbert to Kontsevich: Cut-and-paste equivalence in K-theory, IISER Bhopal, 22 August 2023
Representation theory of quivers, IISER Bhopal, 21 August 2023
Definable combinatorics and Grothendieck rings, Logic Webinar@IITK, 2 Oct. 2020
Actions on the Ziegler spectra of domestic string algebras, Algebra Seminar, University of Manchester, 9 Oct. 2019
Infinities and infinitesimals, Science Coffee House, IITK, 5 Nov 2017
Definable categories, School of Mathematics, University of Manchester, 29 June 2017
Models for regular theories in the additive and non-additive categories, Logic Seminar, University of Manchester, 28 June 2017
Maths on the beach under a palm tree, Stamatics, IITK, 6 Sept 2017
Administrative Responsibilities at IIT Kanpur
- Executive Committee member, Center for Education Research and Teaching Excellence (CERTEX), 2025-26
- Department representative, Institute Digital Infrastructure and Automation Committee (IDIAC), 2024-26
Academic Workshops Attended
Advances in Representation Theory of Algebras (ARTA X), Cologne, Germany, September 2025
Legacy of Peter Gabriel, Bielefeld, Germany, August 2025
AESiM titled Flavours of Representation Theory at North-Eastern Hill University, Shillong, July 25
Calcutta Logic Circle Annual Meet, Kolkata, November 2024
Advances in Representation Theory of Algebras (ARTA IX), Kingston, Canada, June 2023
Indian Conference on Logic and Applications (ICLA) (Virtual mode), March 2021
Indian School on Logic and Applications (ISLA), (Virtual mode), December 2020
Indian Conference on Logic and Applications (ICLA), IIT Delhi, March 2019
Indian School on Logic and Applications (ISLA), VIT Vellore, October 2018
Calcutta Logic Circle Annual Meet, Kolkata, October 2017
Indian Conference on Logic and Applications (ICLA), IIT Kanpur, January 2017
Czech, Slovenian, Austrian, Slovak and Catalan Mathematical Societies join meeting, (CSASC 2016), Barcelona, September 2016
Eduard Čech Institute (ECI) meetings in Prague and Telč, 2016
Model theory days, Second University of Naples, Caserta, Italy, November 2015
Summer school and workshop on infinite dimensional representations of finite dimensional algebras, Manchester, September 2015
Topology, Algebra and Categories in Logic (TACL)-2015, Ischia, June 2015
British Postgraduate Model Theory Conference BPGMT-2014, January 2014
Model Theory 2013, Ravello, Italy, June 2013
British Postgraduate Model Theory Conference BPGMT-2013, January 2013
Other Academic Activities
Representation theory of bound quiver algebras, CIMPA-funded AESiM Flavours of Representation Theory at North-Eastern Hill University, Shillong, July 25.
Auslander-Reiten theory, Virtual AIS on Representations of quivers and BGG category O for semi-simple Lie algebras, Dec. 24.
Categorical syntax-semantics dualities, ISLA 2022 Part-I, hybrid mode, May 22.
Completeness and compactness theorems in propositional and predicate logic, ISLA 2020, virtual mode, Dec. 20.
Measure theory, Annual Foundation School-II, Bhaskaracharya Pratishthana, Pune, June 19.
Topology, Annual Foundation School-I, Bhaskaracharya Pratishthana, Pune, Dec. 17, Dec. 18.
Model theory, PG level, Indian School on Logic and Applications (ISLA), Vellore VIT, Sept.-Oct. 18
Introduction to elliptic curves (with G. Terzo), UG level, Second university of Naples, Caserta, Italy, Fall 15
Algebraic K-theory, UG level, Second university of Naples, Caserta, Italy, Spring 15
K-theory of model-theoretic structures, Invited short, Leeds university, March 14
Category theory and Topos theory, Invited graduate level, Pune University, Summer 11
Fundamentals of discrete Fourier transforms for digital image processing, Invited short, Fergusson college and Garware college, Pune, July 11
PhD Supervision
Annoy Sengupta
Thesis: Combinatorial explorations in the category of modules over zero-relation algebras
Shantanu Sardar
Thesis: On the combinatorics of the bridge quiver for string algebras Defense: 6 May 2022