Joint Colloquium: Gannon -- Moonshine: Old and New

40 years ago John Mckay noticed that 196884=196883+1, and Monstrous Moonshine was born.
In 1998 Borcherds won a Fields Medal primarily for his work explaining McKay’s
equation.  5 years ago string theorists Eguchi, Ooguri and Tachikawa observed that
90=45+45, 462=231+231 and 1540=770+770, and Mathieu Moonshine was born.  These new
equations have still not been explained.  My talk will introduce you to these two
moonshines.