Benjamin Steinberg: The representation theory of the full transformation monoid

The representation theory of the symmetric group has been studied for over 100 years and is a rich and fascinating blend of algebra and combinatorics. The representation theory of the full transformation monoid, the monoid of all self-maps of a finite set, goes back nearly 60 years and is an interesting combination of symmetric group representation theory and the modern theory of finite dimensional algebras. In this talk we survey some older developments and some recent ones focusing on the construction of the irreducible representations, the character table, representation type and global dimension. A number of open questions will be discussed.