Publications
Research Publications, Survey Articles (and Preprints)
** All author names are in alphabetical order (by their surname).
(Survey Article) Various Representation Dimensions Associated with a Finite Group (with Ayush Udeep)
Mathematics Newsletter, Ramanujan Mathematical Society, 2024.
Images of polynomial maps with constants (with Saikat Panja and Prachi Saini)
preprint 2023.
Waring problem for triangular matrix algebra (with Rahul Kaushik)
Linear Algebra and Its Applications, Volume 692, 1 July 2024, Pages 135-159. https://doi.org/10.1016/j.laa.2024.03.031
Representation dimension of some finite groups (with Gurleen Kaur and Amit Kulshrestha).
preprint 2023.
Surjectivity of polynomial maps on matrices (with Saikat Panja and Prachi Saini).
preprint 2023.
Powers in finite unitary groups (with Saikat Panja).
accepted Journal of Algebra 2024.
(Survey Article) Differential Central Simple Algebras (with Parul Gupta and Yashpreet Kaur).
To appear, conference proceedings, contemporary mathematics, 2023. preprint
Splitting of differential quaternion algebras (with Parul Gupta and Yashpreet Kaur).
Journal of Algebra Volume 633, 1 November 2023, Pages 43-55. preprint https://doi.org/10.1016/j.jalgebra.2023.06.022
Matrix Waring problem - II (with Krishna Kishore).
accepted, Israel Journal of Mathematics, 2023. preprint
Nilpotent Lie algebras with two centralizer dimensions over a finite field (with Rijubrata Kundu and Tushar Kanta Naik).
Journal of Algebra, Volume 633, 1 November 2023, Pages 362-388. preprint https://doi.org/10.1016/j.jalgebra.2023.06.013
Powers in finite orthogonal and symplectic groups: A generating function approach (with Saikat Panja).
accepted, Israel Journal of Mathematics, 2023. preprint
Splitting fields of differential Symbol Algebras (with Parul Gupta and Yashpreet Kaur).
Journal of Pure and Applied Algebra Volume 227, Issue 5, May 2023, 107280. preprint 2022. https://doi.org/10.1016/j.jpaa.2022.107280
Nilpotent Lie Algebras of Breadth Type (0,3) (with Rijubrata Kundu and Tushar Kanta Naik).
Communications in Algebra, Volume 51 (2023) Issue 9, 3792-3809. preprint. https://doi.org/10.1080/00927872.2023.2188416
Generating functions for the powers in GL(n,q) (with Rijubrata Kundu).
Israel Journal of Mathematics, 2023. preprint https://doi.org/10.1007/s11856-023-2525-5
Branching rules and commuting probabilities for triangular and unitriangular matrices (with Dilpreet Kaur and Uday Bhaskar Sharma).
Journal of Algebra and its Applications 21 (2022), no. 11, Paper No. 2250231, 35 pp. https://doi.org/10.1142/S0219498822502310
(SURVEY ARTICLE) z-classes in groups: a survey (with Sushil Bhunia).
Indian J. Pure Appl. Math. 52 (2021), no. 3, 713-720. https://doi.org/10.1007/s13226-021-00186-6
Asymptotics of the powers in finite reductive groups (with Amit Kulshrestha and Rijubrata Kundu).
Journal of Group Theory, 25 (2022), no. 6, 1149–1172. https://doi.org/10.1515/jgth-2020-0206
p-power conjugacy classes in U(n,q) and T(n,q) (with Silvio Dolfi and Manoj K. Yadav).
Journal of Algebra and its applications Vol. 20, No. 07, 2150121 (2021) https://doi.org/10.1142/S0219498821501218. preprint.
(SURVEY ARTICLE) Commuting probability and simultaneous conjugacy classes of commuting tuples in a group (with Uday Bhaskar Sharma)
Mathematics Newsletter, Ramanujan Mathematical Society, vol 31, no 1, 2020.
(SURVEY ARTICLE) Two generation of finite simple groups (with Yash Arora).
The Mathematics Consortium Bulletin Vol. 1, Issue 4, April 2020. preprint.
Algorithms in Linear Algebraic Groups (with Ayan Mahalanobis; Sushil Bhunia; Pralhad Shinde).
Adv. Appl. Clifford Algebras 30, 31 (2020). https://doi.org/10.1007/s00006-020-01054-y
Finiteness of z-classes in reductive groups (with Shripad M. Garge).
Journal of Algebra, 554 (2020) 41-53. https://doi.org/10.1016/j.jalgebra.2020.01.010 Arxiv
Branching rules for unitary and symplectic matrices (with Uday Bhaskar Sharma).
Communications in Algebra 2020, vol. 48, no. 7, 2958-2985. https://doi.org/10.1080/00927872.2020.1726366
Computing n-th roots in SL_2 and Fibonacci polynomials (with Amit Kulshrestha).
Proc. Indian Acad. Sci. Math. Sci. 130 (2020), no. 1, 31. https://doi.org/10.1007/s12044-020-0559-8 arXiv. (see a review of this paper on zbMATH by B Sury)
On Shalev's conjecture for type A_n and {}^{2}A_n (with Alexey Galt, Amit Kulshrestha and Evgeny Vdovin).
Journal of Group Theory, 22 (2019) 713-728. https://doi.org/10.1515/jgth-2018-0142. Arxiv.
z-classes and rational conjugacy classes in alternating groups (with Sushil Bhnuia and Dilpreet Kaur).
Journal of Ramanujan Math. Soc. 34, No.2 (2019) 169–183. Arxiv.
Conjugacy Classes of centralizers in unitary groups (with Sushil Bhunia).
Journal of Group Theory, 22 (2019), 231-251. https://doi.org/10.1515/jgth-2018-0036. Arxiv.
Gaussian elimination in split unitary groups with an application to cryptography (with Ayan Mahalanobis).
Journal of Algebra Combinatorics Discrete Structure and Applications, 4 (3) 2017, 247-260. http://dx.doi.org/10.13069/jacodesmath.327373. arXiv
Strongly Real Classes in Finite Unitary Groups of odd characteristic (with Zachary Gates and C. Ryan Vinroot).
Journal of Group Theory 17 (2014), no. 4, 589-617. https://doi.org/10.1515/jgt-2014-0010. Arxiv
(SURVEY ARTICLE) Real elements and Schur indices of a group (with Amit Kulshrestha).
The Mathematics Student, Vol 80, No.s 1-4 (2011) 73-84. schur-indices-real-elements.pdf
Real and Strongly Real Classes in PGL_n(q) and quasi-simple Covers of PSL_n(q) (With Nick Gill).
Journal of Group Theory 14 (2011), 461–489. https://doi.org/10.1515/jgt.2010.055
Real and Strongly Real Classes in SL_n(q) (with Nick Gill).
Journal of Group Theory 14 (2011), 437–459. https://doi.org/10.1515/jgt.2010.054
Conjugacy Classes of Centralizers in G_2.
Journal of Ramanujan Mathematical Society, 23 no. 4 (2008), 327-336. con_cent_g2.pdf
Reality Properties of Conjugacy Classes in Algebraic Groups (with M. Thakur).
Israel Journal of Mathematics 165 (2008), 1-27. https://doi.org/10.1007/s11856-008-1001-6
Reality Properties of Conjugacy Classes in G_2 (with Maneesh Thakur).
Israel Journal of Mathematics 145 (2005), 157-192. https://doi.org/10.1007/BF02786689
Books and Book Chapters
The MOR Cryptosystem in Classical Groups with a Gaussian Elimination algorithm for Symplectic and Orthogonal Groups (Sushil Bhunia, Ayan Mahalanobis and Pralhad Shinde) book chapter in Modern Cryptography - Theory, Technology, Adaption and Integration 2019 ISBN 978-1-78984-417-9.
From Linear Algebra to Matrix Groups -- An exercises based approach to matrix groups (now also available through AMS Open Math Notes OMN:202009.110854)
Class Notes on Representation Theory of Finite Groups (December 2009, revised December 22)
Some other Articles
Asymptotics of commuting probabilities in reductive algebraic groups (with Shripad M. Garge and Uday Bhaskar Sharma).
Constructing Quaternions.
Real and Strongly Real Classes in Finite Linear Groups (with Nick Gill), arxiv math.GR 0809.4412.
Real Elements in Spin Groups (Preprint) Real_Spin.pdf
Some Notes
Various Representation Dimensions associated to a Finite Group, talk at HRI December 2023.
Solving Equations, talk in MSDEED IISER Pune November 23.
Classification of finite simple groups (written for Science club "Helicase" magazine)
Asymptotics of powers in finite reductive groups (IMSc Algebraic Combinatorics Seminar)
Strongly real elements in the finite Unitary group (talk at Manchester)
Quaternions (Lecture given in Madhava at BP on 10May 2012)
Classification of Finite Simple Groups : Tits and Thompson won Abel Prize 2008 (talk given in Science Club, IISER Pune, 4 November 2008) Classification-Simple.pdf
Algebraic Preliminaries - Reductive Algebraic Groups - II (notes on chapter 11 of Springer's book on Algebraic groups, May 2008) reductivegroups.pdf
Real Elements in Algebraic Groups (talk given by me in Transformation Groups 2007, Moscow) TG07_fullscreen.pdf
Reality Properties of Conjugacy Classes in Algebraic Groups. PhD-thesis.pdf
Notes from a course on Number Theory given by Dipendra Prasad at HRI in 2001. alg_no_th.pdf
Elementary exercises on Algebraic groups. exercises_alg_gp.pdf
Tiling (a presentation given to high school kids on open day in TIFR December 2007) tiling.pdf