Dr Jayanta Manoharmayum

School of Mathematical and Physical Sciences

Lecturer

J.Manoharmayum@shef.ac.uk
+44 114 222 3871

Full contact details

Dr Jayanta Manoharmayum
School of Mathematical and Physical Sciences
J22
Hicks Building
Hounsfield Road
Sheffield
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

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Journal articles

All publications

Journal articles

Conference proceedings papers

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

Preprints

  • Manoharmayum J (2024) The Artin--Rees lemma and size of spaces over nonassociative complete filtered rings. RIS download Bibtex download
Research group

Number Theory

Grants

Past grants, as Principal Investigator

Modularity and Galois Respresentation of Totally Real Fields - Nuffield

Teaching activities
MAS110 Mathematics Core I