Automatic Continuity from a personal perspective

Abstract: 

Automatic Continuity is a unique area which combines in an intricate way elements of analysis, algebra, and topology. We ask whether if a map T from X to Y satisfies an algebraic condition that implies that T is continuous.

We will discuss the history of this area of mathematics, several examples, as well as open problems. We assume that the audience is familiar with the basics of functional analysis but no prior knowledge of automatic continuity is assumed.