Pansu differentiability does not imply differentiability

Following my last talk on the notion of Pansu differentiability on Carnot groups, I will present an extreme example of a continuously Pansu differentiable function on the Heisenberg group which is not even approximately differentiable in the Euclidean sense anywhere on a set of positive measure. This example, which is due to Valentino Magnani and is based on a technique developed by Kirchheim and Cassano, exhibits a fundamental difference between the two notions of differentiability of functions on non-commutative Carnot groups.