Jason Saied, Rutgers University

Abstract

The Rogers-Ramanujan identities are a pair of deep partition identities that were first proven by Rogers in 1894 and (independently) Ramanujan in 1917. In the following years, a variety of different proofs were given, but they mostly took the form of verifications: the proofs relied on having guessed or been given both sides of the identities in advance. We will discuss an argument called the "motivated proof," first given by Andrews and Baxter in 1989, in which they proved the Rogers-Ramanujan identities by starting with only one side of the identities. It is very cool, different from anything else I have seen, and doesn't openly use any algebra. (At the very end, I will try to ruin it by explaining how it might connect to algebra after all.) If you know what a generating function is, you should understand everything except the last 5-10 minutes.

See: https://sites.math.rutgers.edu/~qcd2/GCS.html  

Presented via Zoom - Meeting ID: 984 4140 9199

https://rutgers.zoom.us/j/98441409199

Password: 715004