[Algebra Seminar] 196884=196883+1
SPEAKER | Kim, Hyun Kyu
INSTITUTE | KIAS
DATE | March 12(Thu), 2015
TIME | 10:30
PLACE | 1423
ABSTRACT | In late 1970's John McKay discovered the astonishing identity 196884=196883+1, which lead Conway and Norton to formulate the famous Monstrous Moonshine conjectures about the Monster group, the largest sporadic finite simple group. The simplest part of the conjecture is about the existence of a natural infinite dimensional Z-graded representation of the Monster, with the dimensions of the graded pieces coinciding with the coefficients of the j-function in number theory. Such a module was constructed by I.Frenkel-Lepowsky-Meurman in mid 80's with an additional algebraic structure - a vertex operator algebra - whose full automorphism group is proved to be the Monster. Later most of these conjectures were proved by Borcherds.
I will give an elementary historical introduction to formulation of these conjectures and some of the subsequent mathematical developments. So I will first present some coincidences from number theory and the theory of finite simple groups, and then sketch the underlying idea of the theory of vertex operator algebras, in relation to conformal field theory. The discussion on the vertex operator algebras will be only very cursory, and hence will NOT be very detailed and precise. Most of the talk will be focused on understanding the original conjecture itself. Throughout the talk, some knowledge on basic complex analysis is assumed.
This talk is planned to be videotaped and uploaded to the KIAS video archives.