MAT 678: Analysis on metric spaces.

We will review some analysis in Euclidean spaces and then continue to generalize it to the setting of metric spaces. One goal will be to understand Cheeger's result, saying that metric spaces which are not too bad, admit differentiable structures. Another goal will be to understand some basic facts about quasisymmetric maps. On route will will need to go over things such as covering theorems, Lipschitz functions, doubling measures, maximal functions, modulus, upper gradient, Sobolev spaces, Poincare inequality, quasisymmetric maps, etc.