Properties of certain sets of functions having special properties Richard M. Aron

We discuss work with Vladimir Gurariy and Juan Seoane, in which it is shown that the set of everywhere differentiable, nowhere monotone functions f : R → R contains an infinite dimensional vector space. We also hope to discuss recent work (by others) involving the set of entire functions f : C → C such that the set {f(z), f(z + a), ..., f(z + na), ...} is dense in H(C).