Dr Shushma Rani

Assistant Professor
  • Department of Mathematics
  • Indian Institute of Technology Ropar
  • Rupnagar, Punjab - 140001, India
  • Office: C-319, Third Floor, Block-C, SAB building
  • Phone: 0188123-2335 (O)
  • Email: shushmarani@iitrpr.ac.in
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Dr. Shushma Rani earned her PhD in Mathematics from IISER Mohali in 2023. Her doctoral research focused on representations and structures of infinite-dimensional Lie algebras. She looks forward to advancing in this intriguing field of infinite-dimensional Lie (super)algebras and developing new insights.
  • Ph.D from Indian Institute of Science Education and Research Mohali, India, 2023
  • M.Sc in Mathematics, Punjabi University, Patiala, India
  • Assistant Professor, IIT Ropar – Dec 2025 – Till Present
  • Postdoctoral Fellow, IISc, Bangalore, India, Sept.-2024 to Dec-2025
  • Postdoctoral Fellow, HRI, Allahabad, India, Sept-2023 to Aug-2024

7.  Tanusree Khandai, Shushma Rani, Graded Character Formula for Fusion Products of Irreducible Modules and Littlewood-Richardson Coefficients in Type A2, accepted for publication in Journal of algebra and its applications, 2026.

6. Niranjan Nehra, Shushma Rani, 2-local derivations on symmetrizable Kac-Moody Lie algebras, Algebra Colloquium, 33(2), 217-222, 2026.

5. Shushma Rani, Niranjan Nehra, Rohit Garg, On commuting automorphisms of nilpotent Lie algebras, Communications in Algebra, 54(3), 1305–1313, 2026.

4. Shushma Rani, Divya Setia, Graded representations of current Lie superalgebra sl(1|2)[t], Linear Algebra and its applications, 727, 178-202, 2025.

3. Divya Setia, Shushma Rani, Tanusree Khandai, Filtration of tensor product of local Weyl modules for sl_{n+1}[t], J Algebr Comb, 61, 54, 2025.

2. Shushma Rani, G. Arunkumar, A study on free roots of Borcherds-Kac-Moody Lie superalgebras, J. Combin. Theory Ser. A., 204: 105862, 2024.

1. Niranjan Nehra, Shushma Rani, Image of Lie polynomial of degree 2 evaluated on Nilpotent Lie algebras, Communications in Algebra, 51(1), 46-62, 2023.

21. On “Beyond Graphs: Marked Chromatic Polynomials and Independence Series”, at IWM Annual conference-2026, IISER Mohali from July 9-11, 2026.

20. Presented a poster at Integrable combinatorics summer school, Institute of Mathematics Jussieu-Paris Rive Gauche (IMJ-PRG) from June 15-19, 2026.

19. On “Marked Multi-coloring and Marked Chromatic polynomials for Hypergraphs,” at MERU 2026 international conference, IIT Bhilai, from June 1-3, 2026

18. On “Weyl-modules and CV-modules of Lie superalgebras sl(1,2)[t],” at Combinatorics, Geometry, and representation theory Conference, ICTS Bangalore from November 17-30, 2025.

17. On “Graded Representations of current Lie superalgebras,” at Departmental seminar, IISER Mohali on July 22, 2025.

16. Presented a poster at the Modern trends in non-associative algebras, CIMPA school in Tashkent, Uzbekistan from April 30- May 9, 2025.

15. Presented a poster at $11^{th}$ Heidelberg Laureate Forum 2024, Germany, September 22-27, 2024.

14. On “Commuting automorphisms of nilpotent Lie algebras” at World of Group Craft IV on September 9, 2024.

13. On “Generalized $k$ Chromatic polynomials and root multiplicities of BKM Lie superalgebras” at International Conference on Enumerative Combinatorics and Applications (ICECA 2024) held in virtual mode on August 26-28, 2024.

12. Contributed talk at Indian Women and Mathematics (IWM), annual Conference 2024, held at BITS Pilani, Goa on July 11, 2024.

11. Delivered two lectures on “Derivatives” in Scientific Hindi Workshop organized by Rajbhasha Section, HRI, for $12^{th}$ standard students on July 8-9, 2024.

10. On commuting automorphisms of nilpotent Lie algebras at Math department seminar, IISER Mohali, on $20^{th}$ June 2024.

9. On “Filtration of tensor product of local Weyl modules by fusion modules” at Lie theory seminar, University of California Riverside, USA, on 9th May 2024.

8. On “Free root spaces of Borcherds-Kac-Moody Lie superalgebras” at BIU representation theory Seminar, Bar Ilan University, Israel on 17th January 2024.

7. On “Generalized $k$ Chromatic polynomials and root multiplicities of Borcherds-Kac-Moody Lie superalgebras“, at International conference Algebraic and Combinatorial Methods in Representation Theory, ICTS Bengaluru, on November 16, 2023.

6. On “Fusion product modules of current Lie algebra of type $A_2$” at Mathematics Seminar, HRI Prayagraj (Allahabad), India on November 7, 2023.

5. On “Current Lie Algebra and its graded representations” at Mathematics Seminar, HRI Prayagraj (Allahabad), Uttar Pradesh, India on November 6, 2023.

4. On “Tensor product multiplicities and CV modules for current Lie algebra of $\mathfrak{sl}_3$” at Young Mathematician’s Symposium, 2023 (YoMaths-$2023!$) held at Department of Mathematics, IISER Mohali on May 8, 2023.

3. On “Free root spaces of Borcherds-Kac-Moody Lie superalgebras” at Algebraic-combinatorics Seminar held at Department of Mathematics, IISc Bangalore on January 11, 2023.

2. On “Filtration and Graded decomposition of Fusion product modules of current Lie algebra $\mathfrak{sl}_3[t]$” in Young Mathematician’s Symposium 2022 (YoMaths-2022!) at Department of Mathematics, IISER Mohali on May 7, 2022.

1. On “Combinatorial viewpoint of root spaces of Borcherds-Kac-Moody Lie superalgebra $\mathfrak{g}$” at CUP-IISERM Mathematics Graduate Student Workshop held virtually at the Central University of Punjab and IISER Mohali on December 15, 2020.

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