Andrew Schopieray (University of New South Wales) Friday 13 October, 12-1pm, Place: Carslaw 375 Title: Symmetries of the Weyl Alcove. Abstract: The representation theory of quantum groups at roots of unity provides endless examples of braided fusion categories whose combinatorics are "truncated" versions of the classical story. In general this truncation produces an abundance of symmetry, which can be used to study their module categories. In this talk we will survey known results and outline several open questions.