Jon Bevan will be giving a talk in the PDE seminar at Oxford on Monday 14th January on “N-covering stationary points and constrained variational problems”.  The talk will show how degree N maps of the form u_N(z) = frac{z^N}{|z|^{N-1}}} arise naturally as stationary points of functionals like the Dirichlet energy. Moreover it is shown that functions of this form are minimizers of related variational problems, including one whose associated Euler-Lagrange equation bears a striking resemblance to a system studied by N Meyer in the 1960s, and another where the constraint det{nabla u}=1 a.e. plays a prominent role.