My research domain consists of various topics:
I) Iwasawa theory (most of my papers are dedicated to this topic)
II) p-adic Langlands program, specifically multivariable étale (varphi-gamma) modules. (see paper 10 below)
III) rigid analytic automorphic representations (the papers 4 and 5 are dedicated to this topic)
IV) big image Galois representation of general reductive groups (the paper 7 is dedicated to this topic)
V) p-rational number fields and numerical computations (the paper 8 studies Greenberg's conjecture on p-rational fields. Note that parts of this paper uses Cohen-Lenstra heuristics and Bartel and Lenstra (Proc. London Math. Soc. (3), 121, 2020) have now disproven the original Cohen-Lenstra-Martinet heuristics, making essential use of the main conjectures of Iwasawa theory.)
Jishnu Ray, Explicit ring-theoretic presentation of Iwasawa algebras, Comptes Rendus Mathématique, 356. Issue 11-12:1075-1080, 2018.
Jishnu Ray, Presentation of the Iwasawa algebra of the first congruence kernel of a semi-simple, simply connected Chevalley group over Zp, Journal of Algebra, 511:405–419, 2018.
Jishnu Ray, Explicit presentation of an Iwasawa algebra: The case of pro-p Iwahori subgroup of SLn(Zp), Forum Mathematicum, 32(2):319–338, 2020.
Jishnu Ray, Globally analytic principal series representation and Langlands base change, Pacific Journal of Mathematics, Vol. 307, No. 2, 455–490, 2020.
Jishnu Ray, Rigid analytic vectors of crystalline representations appearing in p-adic Langlands, Journal of Number Theory, volume 238, pages 82-105, September 2022.
Jishnu Ray. On the growth of \mu-invariant in Iwasawa theory of supersingular elliptic curves, Acta Arithmetica, 202 (2022), 241-251.
Papers in collaboration:
Christophe Cornut and Jishnu Ray, Generators of the pro-p Iwahori and Galois representations, International Journal of Number Theory, 14(1):37–53, 2018.
Razvan Barbulescu and Jishnu Ray, Numerical verification of the Cohen-Lenstra-Martinet heuristics and of Greenberg’s p-rationality conjecture, Journal de Théorie des Nombres de Bordeaux, Tome 32 (2020) no. 1, pp. 159-177.
Dong Han, Jishnu Ray and Feng Wei, Normal elements in the Iwasawa algebra of Chevalley groups, Manuscripta Mathematica, June 2020.
Jishnu Ray, Feng Wei and Gergely Zábrádi, Multivariable (φ,Γ)-modules and representations of products of Galois Groups: The Case of Imperfect Residue Field, Bull. Soc. Math. France 149(3) (2021), 521-546, arxiv link: https:// arxiv.org/abs/2005.11887.
Parham Hamidi and Jishnu Ray, Conjecture A and μ-invariant for Selmer groups of supersingular elliptic curves, Journal de Théorie des Nombres de Bordeaux, Volume 33 (2021) no. 3.1, pp. 853-886.
Jeffrey Hatley, Debanjana Kundu, Antonio Lei, Jishnu Ray, Control theorems for fine Selmer groups, and duality of fine Selmer groups attached to modular forms, The Ramanujan Journal 60, pages 237–258 (2023).
Jishnu Ray and Ramdorai Sujatha, Selmer groups of elliptic curves over the PGL(2) extension, Nagoya Mathematical Journal, 248, (2022), 922-938, (https://www.doi.org/10.1017/nmj.2022.14).
Antonio Lei and Jishnu Ray, Iwasawa theory of automorphic representations of GL(2n) at non-ordinary primes, Research in the Mathematical Sciences 10, Article number: 1 (2023), (https://doi.org/10.1007/s40687-022-00360-0).
Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Tadashi Ochiai, Jishnu Ray, A formal model of Coleman families and applications to Iwasawa invariants, Ann. Math. Québec 48 (2024), no. 2, 453–475, (https://doi.org/10.1007/s40316-023-00217-0).
Jishnu Ray and Florian Sprung, On characteristic power series of dual signed Selmer groups, Annales de I'Institut Fourier, Tome 75, no. 6 (2025), p. 2341-2357, (https://doi.org/10.5802/aif.3702).
Jishnu Ray and Florian Sprung, On the signed Selmer groups for motives at non-ordinary primes in ℤ_p^2-extensions, Journal of Number Theory, Volume 276, November 2025, Pages 209-231, (https://doi.org/10.1016/j.jnt.2025.02.011).
Papers with PhD students:
Cédric Dion and Jishnu Ray, On the Mordell-Weil Ranks of supersingular abelian varieties over ℤ_p^2-extensions, to appear in Israel Journal of Mathematics, (http://arxiv.org/abs/2112.00280).
This paper was a part of Cédric Dion's PhD thesis at Université Laval, Québec, Canada.
Jishnu Ray and Selvam V, Selmer companion symmetric square representations of modular forms, to appear in The Ramanujan Journal.
This paper will be a part of Selvam's PhD thesis at Harish-Chandra Research Institute.
Papers with postdocs:
Aranya Lahiri and Jishnu Ray, Presentation of an Iwasawa algebra:The pro-p Iwahori of simple, simply connected, split groups, Canadian Mathematical Bulletin Volume 68, Issue 2, June 2025, pp. 377 - 394, (http://dx.doi.org/10.4153/S000843952400078X).
Aranya Lahiri is a postdoc at Indiana University, Bloomington, USA.
Sohan Ghosh, Jishnu Ray and Takashi Suzuki, Finiteness and cofiniteness of fine Selmer groups over function fieds, Proceedings of the American Mathematical Society, Volume 153, Number 10, October 2025, Pages 4225–4238 (https://doi.org/10.1090/proc/17300).
Sohan Ghosh and Jishnu Ray, On Selmer groups over Greenberg neighbourhoods in the function field case, to appear in Ann. Math. Québec.
Sohan Ghosh was a postdoc at HRI during 2022-2024.
Preprints in collaboration:
Sohan Ghosh, Jishnu Ray and Takashi Suzuki, On μ-invariants and isogenies for abelian varieties over function fields, arxiv link: https://arxiv.org/abs/2407.21431.
Matteo Longo, Jishnu Ray and Stefano Vigni, On anticyclotomic Selmer groups of elliptic curves, arxiv link: https://arxiv.org/pdf/2504.01696.
Single author preprints:
Jishnu Ray, On signed Mordell-Weil groups for abelian varieties, arxiv link: https://arxiv.org/abs/2304.13452.
Jishnu Ray, On a parity result for the symmetric square of modular forms with congruent residual representations, arxiv link: https://arxiv.org/abs/2406.03050.