Mathematics Colloquium: Baileys Lemma

2017-03-27

4:10pm Neill Hall 5W

Chris Jennings-Shaffer

I will discuss Baileys Lemma, one of my favorite tools in the study of basic hypergeometric series (q-series). We give with a brief introduction to q-series and the history of Baileys Lemma, beginning with the celebrated Rogers-Ramanujan identities. To illustrate the widespread usage of these identities, we very briefly discuss their role is solving the hard hexagonal model of statistical mechanics. We then return to the role of Baileys Lemma is proving the Rogers-Ramanujan identities and other q-series identities. We see a major use is to aid in determining the modularity of a given q-series. We end by considering a list of series and for each asking the question, is it modular? Refreshments served at 3:30 p.m. Hacker Lounge (Neill 216)