Joseph Baine (USyd) will be speaking in the algebra seminar this week. Joe will be presenting the work of his PhD thesis---please come to celebrate his accomplishment! We will hold a lunch in his honor after the talk, everyone is very welcome to join. Where: Carslaw 275 When: Friday 27 September, 12-1pm Title: (Co)Minuscule Hecke Categories Abstract: Categories whose Grothendieck groups are isomorphic to a Hecke algebra H or a H-module are known as Hecke categories. Two extremely important classes of Hecke categories are the categories of parity sheaves and mixed tilting sheaves on a (partial) flag variety. In this talk we consider these Hecke categories when the partial flag variety is minuscule or cominuscule. In particular, we completely determine the antispherical p-Kazhdan-Lusztig bases in all characteristics, and the spherical p-Kazhdan-Lusztig bases in good characteristic. The antispherical 2-Kazhdan-Lusztig theory of cominuscule Hecke categories is shown to be as complicated as it can be. These are the only examples (outside dihedral groups) of Hecke categories whose p-Kazhdan-Lusztig theory can now be said to be understood.