In this talk, we will present two kinetic models that are used to describe the evolution of charged particles in plasmas: the Vlasov-Poisson system and the Vlasov-Poisson system with massless electron...
Over the recent years deterministic interacting-particle approximations of gradient flows in Wasserstein and other geometries have gained popularity in applications to machine learning and other areas...
Nonlocal shape optimization problems involving interaction energies with competing repulsive and attractive terms are of interest in a variety of applications and have been extensively studied in the ...
We discuss in two relevant case-studies the rigorous derivation via Gamma-convergence of asymptotic energies accounting for singularities in elastic materials from non-local models (convolution-type i...
We consider the open unit disk \(\mathbb{D}\) equipped with the hyperbolic metric and the associated hyperbolic Laplacian \(\mathcal{L}\). For \(\lambda \in \mathbb{C}\) and \(n \in \mathbb{N}\), a ...
Practical Asymptotics is an effective tool for reducing the complexity of large-scale applied-mathematical models arising in engineering, physics, chemistry, and industry, without compromising their a...
Riporterò i risultati di un lavoro in collaborazione con Grushevsky, Salvati Manni e Tsimerman. In tale lavoro classifichiamo le sottovarietà olomorfe compatte massimali di A_g e determiniamo la massi...
In the realms of analysis and geometry, geometric and functional inequalities are of paramount significance, influencing a variety of problems. Traditionally, the focus has been on determining precise...
The Sobolev regularity of solutions to the Monge-Ampère equation in the plane can be rephrased in terms of a unique continuation property of differential inclusions. After an overview of the known res...
One possible framework in which to study the Plateau problem is by using currents with mod(p) coefficients, for a fixed integer p. This setting allows for minimizing surfaces to exhibit codimension 1 ...
