We study some qualitative properties of the solutions to a segregation limit problem in planar domains. The main goal is to show that, generically, the limit configuration of N competing populations consists of a partition of the domain whose singular points are (N-2) triple points, meaning that at most three populations meet at any point on the free boundary. To achieve this, we relate the solutions of the problem to a particular class of harmonic maps in singular spaces, which can be seen as the real part of certain holomorphic functions. The genericity result is obtained by tricky perturbation arguments. 

This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001