Mathematics

Dr.Shaunak Deo
TIFR

One of the main themes of deformation theory of Galois representations is to study families of Galois representations obtained by interpolating various Galois representations having certain prescribed properties. In this talk, I will first review some basic facts and results of deformation theory of Galois representations. Then I will describe the basic anatomy of theorems comparing various universal deformation rings with appropriate Hecke algebras (which are popularly known as 'R=T' theorems in the literature and are important from Number theoretic point of view). In the second half of the talk, I will describe some of my own results in which establishing an R=T theorem has played a crucial role.