Department of

August 2017September 2017October 2017 Su Mo Tu We Th Fr SaSuMo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 5 1 2 1 2 3 4 5 6 7 6 7 8 9 10 11 12 3 4 5 6 7 8 9 8 9 10 11 12 13 14 13 14 15 16 17 18 19 10 11 12 13 14 15 16 15 16 17 18 19 20 21 20 21 22 23 24 25 26 17 18 19 20 21 22 23 22 23 24 25 26 27 28 27 28 29 30 312425 26 27 28 29 30 29 30 31

Friday, September 22, 2017

**Abstract:** In 1999, Cheeger proved that doubling metric measure spaces admitting a Poincare inequality carry a 'measurable differentiable structure' with respect to which Lipschitz functions could be differentiated almost everywhere. A major consequence of this theorem is that if such a space were to biLipschitz embed into a finite dimensional normed space (or as was later proved, any RNP space), a generic point would have all of its tangent cones biLipschitz equivalent to some finite dimensional normed space. We'll outline the proof of this consequence and discuss its application to Carnot groups and inverse limits of graphs.