Event Type:

Department Colloquium

Date/Time:

Friday, January 19, 2007 - 07:00

Location:

Kidd 364

Local Speaker:

Abstract:

Some of the most fascinating mathematics occur when seemingly unrelated objects reveal themselves to be distinctly intertwined. In this talk we will see a surprising connection between the Monster, the largest finite sporadic simple group, and Rogers-Ramanujan functions, which are connected to Ramanujan's famous continued fraction.

One of the many things Ramanujan did in his life was to list 40 identities involving what are now called the Rogers-Ramanujan functions on one side, and products of functions of the form ∏ (1-q^{mn}) (with n=1 to ∞) on the other side. It was remarked by Birch that these identities seemed too complicated to guess, even for one with Ramanujan's incredible instinct for formulae. Recently however, Koike devised a strategy for finding (but not proving) these types of identities by noticing an interesting connection to the Monster. He was able to conjecture many new Rogers-Ramanujan type identities which we have now proved. The key to tying it all together? Modular forms!