Mathematics

Dr Shaunak Deo
TIFR MUMBAI

Abstract: Given a 2-dimensional dihedral representation of a profinite
group over a finite field, we will give necessary and sufficient
conditions for its universal deformation to be dihedral. We will then
specialize to the case of absolute Galois group of a number field and
give sufficient conditions for the universal deformation unramified
outside a finite set of primes to be dihedral. We will also see its
applications to unramfied Fontaine-Mazur conjecture and to an R=T
theorem (in the spirit of Calegari-Geraghty) in the setting of Hilbert
modular forms of parallel weight one. We will begin with a brief
introduction to the deformation theory of Galois representations. This
talk is based on joint work with Gabor Wiese.