I will give the Seminar’s tenth talk for Semester 1 tomorrow morning on Zoom. Please find the details below. Anyone who would like to attend the talk or join the mailing list is warmly invited to e-mail email@example.com. Abstract: This talk will introduce the basics of Kazhdan--Lusztig theory in the setting of sheaves on the flag variety G/B of a reductive group G. In the first section, we will discuss equivariant sheaves and the equivariant derived category in a general framework. We then specialise the context to G/B, whose geometric properties we describe, before defining the Hecke algebra H and the convolution bifunctor. Our final objective is to state and understand the importance of the categorification theorem linking H to B-equivariant sheaves on G/B. Time and date: 11 am Tuesday 25 May.