CFT, strings and Moonshine

By Kishore Marathe (Brooklyn Collegue, New York)

Thirty years ago some very surprising relations between the Fourier coefficients of the Jacobi Hauptmodul or the J-function and representations of the largest finite simple sporadic group, the Monster were discovered. Precise formulation of these relations is now called the ’Monstrous Moonshine’. It has given rise to a large body of new research relating conformal field theory and string theory in physics to geometry and topology in mathematics. We will survey these recent developments and indicate directions for future research.