In this seminar we present a mathematical model to describe the evolution of a city, which is determined by the interaction of two large populations of agents, workers and firms. The map of the city i...
In this talk, I will present recent results on the contact process on two specific types of scale-free, inhomogeneous random networks that evolve either through edge resampling or by resampling entire...
We consider the optimal regulation problem for nonlinear control-affine dynamical systems. Whereas the linear-quadratic regulator (LQR) considers optimal control of a linear system with quadratic cost...
We will introduce and discuss a notion of s-fractional mass for 1-currents, generalizing the s-fractional perimeter in the plane to higher codimension singularities. We will present basic compactn...
Deciding whether a given algebraic variety is rational (birational to projective space) is an important problem in algebraic geometry. Over the field of real numbers, this problem is particularly inte...
In this talk I will present a recent work in which the strong ill-posedness of the two-dimensional Boussinesq system is proven. I will show explicit examples of initial data with vorticity and densit...
In Catalan percolation, one declares the edges {i,i+1}, for integer i, occupied and each edge {i,j} with j> i+1 open independently with probability p. For k> i+1, we recursively define {i,k} to ...
In this talk we consider a class of scalar nonlinear models describing crowd dynamics. The congestion term appears in the transport equation in the form of a compactly supported nonlinear mobility fun...
We are concerned with a generalization to the singular case of a result of C.C. Chen e C.S. Lin [Comm. An. Geom. 1998] for Liouville-type equations with rough potentials. The singular problem is actua...
We consider radial solutions of fully nonlinear, uniformly elliptic equations posed in punctured balls, in presence of radial singular quadratic potentials. We discuss both the principal eigenvalues p...
Digital models (DMs) are designed to be replicas of systems and processes. At the core of a digital model (DM) is a physical/mathematical model that captures the behavior of the real system across tem...
Suppose that two nonlocal minimal surfaces are included one into the other and touch at a point. Then, they must coincide. But this is perhaps less obvious than what it seems at first glance. This se...
