Fractional derivatives, a widely recognized mathematical tool, have gained considerable attention in recent decades owing to their non-local behavior, particularly suitable for capturing anomalous dif...
We study a system of nonlocal aggregation cross-diffusion PDEs that describe the evolution of opinion densities on a network. The PDEs are coupled with a system of ODEs that describe the time evolutio...
Abstract: Secondo la filosofia della congettura di Green-Griffiths-Lang, ci si aspetta che l'esistenza e la distribuzione dei punti razionali per le varietà che sono uniformemente non-iperboliche...
In this talk I will discuss some results about long time behaviors of solutions to Hamiltonian PDEs (Schrödinger, Kirchhoff, etc). In particular I will focus on a recent result where we (with J. Berni...
We are interested here in questions related to the maximal regularity of solutions of elliptic problems with Dirichlet boundary condition (see [1]). For the last 40 years, many works have been concern...
A discrete and faithful representation of a surface group in PSL(2,C) is said to be quasi-Fuchsian when it preserves a Jordan curve on the Riemann sphere. Classically these objects lie at the intersec...
We discuss a novel class of swarm-based gradient descent (SBGD) methods for non-convex optimization. The swarm consists of agents, each is identified with position, x, and mass, m. There are three key...
We produce complete, non-compact, Riemannian metrics with positive constant \sigma_2-curvature on a sphere of dimension n>4, with a prescribed singular set given by a disjoint union of closed subma...
We study the surface diffusion flow in the flat torus, that is, smooth hypersurfaces moving with the outer normal velocity given by the Laplacian of their mean curvature. This model describes the evol...
Abstract: This talk provides an overview of my research interests which rely on the theoretical and computational aspects of optimal control problems, with a particular emphasis on the Hamilton-J...
Abstract: In this talk we will review some recent results on the Fröhlich polaron, which is a model for a charged particle coupled to a polarizable medium. We will especially focus on a conjecture due...
