MS Seminar (Mathematics - String Theory)

Speaker: Scott Carnahan (IPMU)
Title: Borcherds products in monstrous moonshine.
Date: Tue, Sep 14, 2010, 13:15 - 14:45
Place: Seminar Room A
Abstract: During the 1980s, Koike, Norton, and Zagier independently found an infinite product expansion for the difference of two modular j-functions on a product of half planes. Borcherds showed that this product identity is the Weyl denominator formula for an infinite dimensional Lie algebra that has an action of the monster simple group by automorphisms, and used this action to prove the monstrous moonshine conjectures.

I will describe a more general construction that yields an infinite product identity and an infinite dimensional Lie algebra for each element of the monster group. The above objects then arise as the special cases assigned to the identity element. Time permitting, I will attempt to describe a connection to conformal field theory.
Remarks: There will be a 5-minute break after the first 25 min.