Appears in collection : Summer School 2016 - Geometric Analysis, Metric Geometry and Topology

I will discuss whether the Minkowski sum of two compact convex bodies can be made smoother by a generic rotation of one of them. Here "generic" is understood in the sense of Baire category. The main result is a construction of an infinitely differentiable convex plane domain whose Minkowski sum with any generically rotated copy of itself is not five times differentiable.