Cristian Popescu
University of California, San Diego, USA

I will discuss my recent joint work with Rusiru Gambheera, leading to an unconditional proof of an Equivariant Main Conjecture for the Selmer groups of general number fields defined by Burns--Kurihara--Sano. Further, I will discuss two applications of this result: a proof of the Burns--Kurihara--Sano Conjecture on Fitting ideals of Selmer groups and a proof of the refined Coates--Sinnott Conjecture on Fitting ideals of even Quillen $K$--groups of number fields. Our work relies on and improves upon the recent breakthrough results of Dasgupta--Kakde on the Brumer--Stark Conjecture, on which I will comment very briefly.