Sumit Kumar: Overview of the Spectral Reciprocity formulae

In the informal talk, we discuss various spectral reciprocity identities which roughly speaking relate one family (of $L$-values) to another `useful' family (of $L$-values). This has been a trending area of research in number theory in recent years. The first instance of such identity was given by Motohashi relating the fourth moment of the Riemann zeta function to the third moment of the Hecke $L$-values over a family of $GL(2)$ forms.