Seamus Albion Ferlinc: Rogers–Ramanujan-type identities

Speaker: Seamus Albion Ferlinc

Abstract: The Rogers–Ramanujan identities are both a pair of $q$-series identities and a pair of identities for integer partitions discovered independently by Rogers and Ramanujan in the late 19th and early 20th centuries. They afford many different proofs, vast generalisations, and are connected to the representation theory of affine Lie algebras and statistical physics. After a crash-course in integer partitions, I will give a brief history of these identities, touching on some of the highlights of their more than 130-year history. This will finish with a view towards exciting recent developments and conjectures.