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Washington State University

Mathematics Colloquium

Department of Mathematics and Statistics

Neill Hall 5W

March 27, Monday, 4:10 - 5:00 PM

Chris Jennings-Shaffer

Department of Mathematics

Oregon State University

Mathematics Colloquium

Department of Mathematics and Statistics

Neill Hall 5W

March 27, Monday, 4:10 - 5:00 PM

Chris Jennings-Shaffer

Department of Mathematics

Oregon State University

Title: Bailey's Lemma

Abstract: I will discuss Bailey's 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 Bailey's 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 Bailey's 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?

Abstract: I will discuss Bailey's 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 Bailey's 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 Bailey's 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 at 3:30pm in Neill 216