CARMA Colloquium

4:00 pm

Thursday, 22nd Apr 2021

SR118, SR Building (and online via Zoom)

Join via Zoom, or join us in person (max room capacity is 9 people).

3:30pm for pre-talk drinks + snacks, and 4pm for the talk

Prof Ole Warnaar

(School of Mathematics and Physics, The University of Queensland)

Cylindric Partitions and Rogers–Ramanujan Identities

Plane partitions are a two-dimensional analogue of integer partitions introduced by MacMahon in the 1890s. Various generating functions for plane partitions admit beautiful product forms, displaying an unexpected connection to the representation theory of classical groups and Lie algebras. Cylindric partitions, defined by Gessel and Krattenthaler in the 1990s, are an affine analogue of plane partitions.

In this talk I will explain what cylindric partitions are, discuss their connection with the representation theory of infinite dimensional Lie algebras, and describe some recent results on Rogers--Ramanujan-type identities arising from the study of cylindric partitions. No knowledge of representation theory will be assumed in this talk.