Toshiyuki Tanisaki Osaka City University Kazhdan-Lusztig basis and a geometric filtration of an affine Hecke algebra Friday 26th November, 12:05-12:55pm, Carslaw 157. According to Kazhdan-Lusztig and Ginzburg, the Hecke algebra of an affine Weyl group is identified with the equivariant K-group of Steinberg's triple variety. The K-group is equipped with a filtration indexed by closed G-stable subvarieties of the nilpotent variety, where G is the corresponding complex reductive algebraic group. I will talk about my recent result with N. Xi showing that the filtration is compatible with the Kazhdan-Lusztig basis of the Hecke algebra in the case of type A.