The Averaging process (a.k.a. repeated averages) is a mass redistribution model over the vertex set of a graph. Given a graph G, the process starts with a non-negative mass associated to each vertex. ...
I will provide a self-contained variational approach to state some classical and new results in the framework of Aubry-Mather theory. More precisely, I will discuss the expansion by Gamma-convergence ...
In this talk we aim at establishing large deviation estimates for the probability that a simple random walk on the Euclidean lattice (d>2) covers a substantial fraction of a macroscopic body. It tu...
The Schrödinger problem consists in finding the most likely evolution of a system of i.i.d. particles, conditionally on their initial and final configurations. In the last decade this problem has beco...
In 1971 J. Serrin proved that, given a smooth bounded domain Ω⊂Rn and u a positive solution of the problem: −Δu=f(u) in Ω, u=0 on ∂Ω, ∂_νu= constant on ∂Ω, then Ω is necessarily a ball and u is radial...
A crucial issue in capillarity-type problems is understanding the behavior of solutions near singular points in the boundary of the container. In the special case of the relative perimeter functional,...
In this talk we will consider a reverse Faber-Krahn inequality for the principal eigenvalue μ_1(Ω) of the fully nonlinear operator P_{+N}u:=λ_N(D2u), where Ω⊂R^N is a bounded, open convex set, and λ_N...
In [Inv. Math., 1978], Morgan proved that almost every curve in R^3 is the boundary of a unique area minimizing surface. I will show how to extend Morgan's result to surfaces of any dimension and codi...
The fact that the flow of a hypersurface by its mean curvature can be seen as a gradient flow of the surface area has motivated an influential minimizing movement scheme (Almgren-Taylor-Wang, Luckhaus...
We address the problem of reconstructing a real potential $V$ from the Dirichlet-to-Neumann map of a Schrödinger operator $-\Delta + V$ on the boundary of a domain in Euclidean space (the reconstructi...
