The unitary dual of a semisimple Lie group is an old and mysterious open

problem in Lie theory. The solution of this problem is the motivating goal

of the Atlas of Lie Groups and Representations, a project to make available,

through an interactive website, information about semisimple Lie groups.

This talk aims to explain what is involved in determining which

Representations of a Lie group are unitary, using the example of the group A_1

(also known as SL(2)), why a computer program might be helpful, and how the E_8

calculation which received wide media attention last year fits into the picture.