Manoharmayum, Jayanta, Dr

Dr Jayanta Manoharmayum

School of Mathematical and Physical Sciences

Lecturer

j.manoharmayum@sheffield.ac.uk
+44 114 222 3871

J22, Hicks Building

Full contact details

Dr Jayanta Manoharmayum
School of Mathematical and Physical Sciences
J22
Hicks Building
Hounsfield Road
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S3 7RH

Research interests: The absolute Galois group of the rationals is my primary interest. It contains almost all arithmetic information: eg, solutions to explicit diophantine equations (as in Fermat's Last Theorem). The whole group in general is rather too large an object to study; a better way of understanding the Galois group is through its representations, and this brings out deep connections with other mathematical objects (such as modular forms). For example, given a two dimensional representation of the Galois group satisfying `usual conditions', there should be a modular form whose Fourier coefficients are related to the traces of the representation. The precise correspondences are conjecturally given by the conjectures of Artin (complex representations), Fontaine and Mazur (p-adic representations), and Serre (finite characteristic). It is aspects of these conjectures, both over the rationals and in the setting of totally real number fields, that I am most interested in.

Publications

Show: Featured publications All publications

Manoharmayum J (2019) . Glasgow Mathematical Journal, 61(1), 115-150.
Manoharmayum J & Eardley T (2016) . Compositio Mathematica, 152(8), 1725-1739.
Manoharmayum J (2015) . Proceedings of the American Mathematical Society, 143, 2743-2758.

Manoharmayum J (2020) . Communications in Algebra.
Manoharmayum J (2019) . Glasgow Mathematical Journal, 61(1), 115-150.
Manoharmayum J & Eardley T (2016) . Compositio Mathematica, 152(8), 1725-1739.
Manoharmayum J (2015) . Proceedings of the American Mathematical Society, 143, 2743-2758.
Adibhatla R & Manoharmayum J (2012) . Acta Arithmetica, 156, 159-175.
Manoharmayum J (2009) . J NUMBER THEORY, 129(5), 1178-1190.
Jarvis F & Manoharmayum J (2008) . J NUMBER THEORY, 128(3), 589-618.
Manoharmayum J (2004) . B LOND MATH SOC, 36, 216-220.
Dieulefait L & Manoharmayum J (2003) Modularity of rigid Calabi-Yau threefolds over Q. Fields Institute Communications, 38.
Manoharmayum J (2001) On the modularity of certain GL(2)(F7) Galois representations. MATH RES LETT, 8(5-6), 703-712.
Manoharmayum J (1999) Abelian surfaces with level √5 structure. The Asian Journal of Mathematics, 3(3), 677-688.
Manoharmayum J (1999) Pairs of mod 3 and mod 5 representations arising from elliptic curves. MATH RES LETT, 6(5-6), 735-754.

Manoharmayum J (2004) Serre's conjecture for mod 7 Galois representations. MODULAR CURVES AND ABELIAN VARIETIES, Vol. 224 (pp 141-149)

Manoharmayum J (2024) The Artin--Rees lemma and size of spaces over nonassociative complete filtered rings.

Grants: Past grants, as Principal Investigator

Modularity and Galois Respresentation of Totally Real Fields - Nuffield

Teaching activities

MAS110

Mathematics Core I