The quotient structures like the Boolean algebra $\wp(\mathbb N)/Fin$, the Banach space $\ell_\infty/c_0$, and the Calkin C*-algebra $\mathcal B(\ell_2)/\mathcal K(\ell_2)$ appear in different areas of mathematics, but they share many striking structural similarities. They may be viewed as large quotients obtained by identifying objects modulo small perturbations: finite sets, null sequences, or compact operators.

The talk will begin with the analysis of the classical paper of Lech Drewnowski and James Roberts on the primariness of the Banach space $\ell_\infty/c_0$. We will discuss the role of additional set theoretic hypothesis in their argument and survey several related later developments concerning operators on $\ell_\infty/c_0$, automorphisms of quotient structures, and masas in the Calkin algebra.

The emphasis will be on analogies between Boolean algebras, Banach spaces, and operator algebras, as well as on the set-theoretic methods that connect these subjects. Several recent results and open problems concerning massive quotients will also be presented."