Everytopic Seminar

 October 2nd, 2007, 1:40 pm – 3:00pm, Goldsmith 226



Title: Monstrous Lie algebras and generalized moonshine

Speaker: Scott Carnahan, MIT








Monstrous moonshine initially arose about 30 years ago from apparent numerical coincidences between modular functions on the complex upper half plane and linear representations of the monster simple group.  Later computations suggested that certain subgroups of the monster also yielded modular functions when combinations of their irreducible representations were assembled into graded vector spaces and their characters taken. This was codified by Norton in his generalized moonshine conjecture, which asserts the existence of a generalized character that associates a modular function to any commuting pair of elements in the monster. I will describe some recent progress on this conjecture, using a construction of generalized Kac-Moody algebras via orbifold conformal blocks to reduce it to a conjecture that about 50 unknown rational numbers are in fact equal to one.