Geometric Satake correspondence

Let G be a reductive group and Gr_G be its affine Grassmannian.
Following a paper of Mirkovic and Vilonen, I will explain that the
category of G_O-equivariant perverse sheaves on Gr_G is equivalent to
the category of representations of the Langlands dual group of G.
Somewhat surprisingly, this can be taken as the definition of the
Langlands dual group. I will not assume that the listeners are
familiar with perverse sheaves but I will assume some knowledge of
affine Grassmannians.