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, 14 pages, 2025.
A p-converse theorem for real quadratic fields, (with Muskan Bansal, Aprameyo Pal and Guhan Venkat), preprint, arXiv:2504.21799.
Asymptotic Fermat equation of signature (r,r,p) over totally real fields, (with Satyabrat Sahoo), (2025), The Ramanujan Journal, to appear.
2-Selmer companion modular forms, (with Abhishek and Sudhanshu Shekhar), ( 2025), Annales mathématiques du Québec, to appear.
Iwasawa theory of Rankin-Selberg product at an Eisenstein prime, (with Ravitheja Vangala & Sudhanshu Shekhar), Journal of Number Theory, 279, 2026, 348-410.
Hilbert's 10th problem via Mordell curve, (with Debanjana Kundu & Dipramit Majumdar), Canadian Mathematical Bulletin, published online, (2025), 11 pages.
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 and Dipramit Majumdar), The Ramanujan Journal, (2025) to appear..
3-Selmer group, ideal class group and cube sum problem, (with Pratiksha Shingavekar and Dipramit Majumdar), Journal of Number Theory, 277, (2025), 165-200.
Iwasawa theory of fine Selmer groups over global fields, (with Sohan Ghosh and Sudhanshu Shekhar), preprint, arXiv:2201.01751.
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.