This seminar gives graduate students the opportunity to hear and present talks on discrete mathematics, either on topics beyond a standard combinatorics class or on original research. GCS is meant to be a friendly, slightly informal speaking environment where questions are encouraged at all points throughout the talk. We only assume a basic general knowledge of combinatorics (at most, basic combinatorics one might learn in a single semester introductory course), so students in any area are welcome to attend.
Speakers for the GCS are welcome (from the math department, other departments, and elsewhere). Please email Quentin Dubroff at
Generously sponsored by DIMACS.
Click here for information about the seminar and the archive.
| Date: | April 7th, 2021 |
|---|---|
| Speaker: | Jason Saied |
| Time: | 12:15PM |
| Place: | Zoom: please email quentin [dot] dubroff [at] rutgers [dot] edu to be added to the mailing list |
| Title: | Motivated proof of the Rogers-Ramanujan identities |
| 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. |