This is the first lecture in a series of 3 by Arun Ram (University of Melbourne), the other two are on June 16 and 17. Tuesday 14 June, 12-1pm, Place: Carslaw 375 Combinatorics of the Loop Grassmannian I will explain what the loop Grassmannian and the affine flag variety are and how to label their points. This labelling is a refinement of the labelling of crystal bases by Littelmann paths. I’ll show the picture which summarises the connection to the affine Hecke algebra and the spherical affine Hecke algebra. I’ll give a summary of the relationship between Mirkovic-Vilonen cycles and the crystal bases and explain how this is reflected in the path model indexing.