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...
This mini-course is concerned with those PDEs which have a gradient flow structure in the Wasserstein space W_2 and can thus be attacked via the so-called Jordan-Kinerlehrer-Otto scheme, a sequence of...
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...
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...
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 ...
In this talk we will consider phase separations on generalized hypersurfaces in Euclidean space. For a diffuse surface area (line tension) energy of Modica-Mortola type, we prove a compactness and l...
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...
