Somnath Jha

Faculty Building 561

Department of Mathematics and Statistics

Kanpur 208016, India

jhasom at iitk dot ac dot in

(+91)5122596916/ (+91)5126796916

Research:

My broad area of research is number theory and arithmetic geometry. I work on problems related to Iwasawa theory of elliptic curves and modular forms. My research interest includes the study of the Selmer group.

Publications and Preprints:

arXiv link for some of the recent preprints is here.

On some injectivity in relative K_0 groups and applications (with Gergely Zábrádi), in preparation.
On certain root number 1 cases of the cube sum problem, (with Shamik Das), preprint, 2025, arXiv:2508.05361.
A p-converse theorem for real quadratic fields, (with Muskan Bansal, Aprameyo Pal and Guhan Venkat), preprint, arXiv:2504.21799.
Iwasawa theory of fine Selmer groups over global fields, (with Sohan Ghosh and Sudhanshu Shekhar), Mathematische Zeitschrift, (2025), DOI: 10.1007/s00209-025-03863-y.
2-Selmer companion modular forms, (with Abhishek and Sudhanshu Shekhar), Annales mathématiques du Québec, (2025), 21 pages, to appear.
Binary cubic forms and rational cube sum problem, (with Dipramit Majumdar & B. Sury), (2023), Proceedings of the American Mathematical Society, to appear.
√-3-Selmer groups, ideal class groups and large 3-Selmer ranks, (with Pratiksha Shingavekar & Dipramit Majumdar), The Ramanujan Journal, Vol 68, Article No. 67, (2025), 25 Pages.
Iwasawa theory of Rankin-Selberg product at an Eisenstein prime, (with Ravitheja Vangala & Sudhanshu Shekhar), Journal of Number Theory, 279, 2026, 348-410.
Asymptotic Fermat equation of signature (r,r,p) over totally real fields, (with Satyabrat Sahoo), The Ramanujan Journal, Volume 68, Article No. 30, (2025), 24 pages.
Hilbert's 10th problem via Mordell curve, (with Debanjana Kundu & Dipramit Majumdar), Canadian Mathematical Bulletin, 68(3), (2025), 939 - 949.
3-Selmer group, ideal class group and cube sum problem, (with Pratiksha Shingavekar and Dipramit Majumdar), Journal of Number Theory, 277, (2025), 165-200.
Multiplicities in Selmer groups and root number of Artin twists (with Tathagata Mandal & Sudhanshu Shekhar), Journal of Number Theory, 238C, (2022), 147-182.
p^r-Selmer companion modular forms, (with Sudhanshu Shekhar, Dipramit Majumdar), Annales de l'Institut Fourier (Grenoble), 71(1) (2021), 53-87.
Twisting Lemma for Λ-adic modules, (with Sohan Ghosh and Sudhanshu Shekhar), Asian Journal of Mathematics, 25(4) (2021) , 551-564.
Control theorem and functional equation of Selmer groups over p-adic Lie extensions, (with Tadashi Ochiai), Selecta Mathematica (N.S.), 26(5), Article no. 80, (2020), 58 pages
Non-commutative twisted Euler characteristic (with Sudhanshu Shekhar), Münster Journal of Mathematics, 11(1) (2018) 1-12.
Functional equation for the Selmer group of nearly ordinary Hida deformation of Hilbert modular forms, (with Dipramit Majumdar), Asian Journal of Mathematics 21(3) (2017) 397-428.
On twists of modules over non-commutative Iwasawa algebras, (with Tadashi Ochiai, Gergely Zábrádi), Algebra & Number Theory , 10(3) (2016) 685-694.
Algebraic functional equation for Hida family, (with Aprameyo Pal) International Journal of Number Theory, 10(7) (2014) 1649-1674.
Fine Selmer group of Hida deformations over non-commutative p-adic Lie extensions, Asian Journal of Mathematics 16(2) (2012) 353-366.
On the Hida deformations of fine Selmer groups, (with R. Sujatha), Journal of Algebra 338(1) (2011) 180-196.

Teaching:

Elliptic curves, modular forms and congruent number problem (MTH525), Monsoon Semester, 2022-23, IIT Kanpur.
Representation Theory of finite groups (MTH732), Winter Semester 2021-22, IIT Kanpur.
Linear Algebra (MTH 201), Monsoon Semester 2021-22, IIT Kanpur.
Linear Algebra & ODE (MTH 102, Institute core course) Winter Semester 2020-21, IIT Kanpur.
Discrete Mathematics (MTH221 & CS221), Monsoon semester 2020-21, IIT Goa.
Number Theory (MTH215), Monsoon semester 2018-19, IIT Kanpur.
Analytic Number Theory (MTH668), Winter semester 2017-18, IIT Kanpur.
Commutative Algebra (MTH612), Monsoon semester 2017-18, IIT Kanpur.
Abstract Algebra (MTH204), Winter semester 2016-17 and Winter semester 2018-19 IIT Kanpur.
A course in arithmetic (MTH688), Monsoon semester 2016-17, IIT Kanpur.
Algebraic Number Theory (MTH 712), Winter semester 2015-16, Monsoon semester 2019-20, IIT Kanpur.
Functional Analysis and Operator Theory (PS645M) January - March 2015, JNU, Delhi.

Conferences/discussion meetings:

Academic Affiliations:

Faculty member, Department of Mathematics & Statistics, IIT Kanpur, 2015 - .
Visiting faculty on deputation at IIT Goa, Goa, 2020 (concurrently with IIT Kanpur).
Faculty member at School of Physical Sciences, Jawaharlal Nehru University, New Delhi, 2014 - 15.
JSPS postdoctoral fellow at Osaka University, 2012 - 14 . Mentor: Tadashi Ochiai.
MATCH postdoctoral fellow at University of Heidelberg, 2011 -12. Mentor: Otmar Venjakob.

PhD, Tata Institute of Fundamental Research, Mumbai, 2012. Thesis advisor : Sujatha Ramdorai.
M. Math., Indian Statistical Institute, Kolkata, 2004-2006.
B.Sc. (Math. Honours) Ramakrishna Mission Vidyamandira, Belur Math, 2001-2004.

Schooling at Chanchal Siddheswari Institution, Chanchal, Malda, 1989-2001.