Nonconvex interactions in mean-field spin glasses

I will describe a conjecture for the limit free energy of mean-field spin glasses with a bipartite structure, which I could prove to be an upper bound for the true limit. The conjectured limit is described in terms of the solution of an infinite-dimensional Hamilton-Jacobi equation. A fundamental difficulty of the problem is that the nonlinearity in this equation is not convex. I will also question the possibility to characterize this conjectured limit in terms of a saddle-point problem