#### Mar 10, 2021: Seminar by Sudhanshu Shekhar (IIT Kanpur)

Title: $p^r$-Selmer companion modular forms

Speaker: Sudhanshu Shekhar (Department of Mathematics & Statistics, IIT Kanpur)

Date and Time: March 10, 2021; 3:00pm

Abstract : Given two elliptic curves $E_1$ and $E_2$ over a number field $K$, Mazur and Rubin have defined them to be $n$-Selmer companion if for every quadratic twist $\chi$ of $K$, the $n$-Selmer group of $E_1^\chi$ and $E_2^\chi$ over K are isomorphic. We will discuss an analogue of this for modular forms.