Research अनुसन्धान

Research Interests

Galois Theory, Inseparable Field Theory, Root Cluster Theory, Invariant Theory, Inverse Galois Problem, Inverse Problems in Root Cluster Theory, Minimal Generating Sets of Galois Closure, Regular property of Invariant rings, Commutative Algebra, Algebraic Number Theory, Group Theory, Galois Representations, Linear Groups and Projective Linear Groups.

____________________________

Research Publications and Preprints

____________________________

(8) Shubham Jaiswal, Tony J. Puthenpurakal. A Generalization of a Theorem of Nakajima-Landweber-Stong. arXiv preprint. Submitted to journal.

https://arxiv.org/abs/2606.14461, Jun 2026.

____________________________

(7) Shubham Jaiswal. Root Clusters and Multiclusters over Imperfect Hilbertian Fields. arXiv preprint. Submitted to journal.

https://arxiv.org/abs/2606.12660, Jun 2026.

____________________________

(6) Shubham Jaiswal and Tony J. Puthenpurakal. The Regular property of Invariant Rings over Regular Domains. Transformation Groups (2026). (DOI)

https://arxiv.org/abs/2511.12569, Nov 2025.

____________________________

(5) Shubham Jaiswal, M Krithika and P Vanchinathan. On Variants of Inverse Cluster Size Problem & General Magnification. arXiv preprint. Submitted to journal.

https://arxiv.org/abs/2511.11841, Feb 2026.

____________________________

(4) Shubham Jaiswal. Root Clusters over Number fields : Inverse Problems and Applications. arXiv preprint. Submitted to journal.

https://arxiv.org/abs/2505.20238, May 2026.

____________________________

(3) Shubham Jaiswal and P Vanchinathan. On Minimal generating sets of splitting field, Cluster towers and Multiple transitivity of Galois groups. Accepted for publication in Czechoslovak Mathematical Journal.

https://arxiv.org/abs/2505.00672, Jan 2026.

____________________________

(2) Chandrasheel Bhagwat and Shubham Jaiswal. Cluster Magnification, Root Capacity, Unique Chains, Base Change and Ascending Index. Proc. Indian Acad. Sci. (Math. Sci.) (2025) 135:19. (DOI)

https://arxiv.org/abs/2405.06825, Sept 2024.

____________________________

(1) Chandrasheel Bhagwat and Shubham Jaiswal. Right Splitting, Galois Correspondence, Galois Representations and Inverse Galois Problem. J. Ramanujan Math. Soc. 40, No.3 (2025) 229–244.

https://arxiv.org/abs/2403.14316, March 2024.

____________________________