Abstract: I will discuss the existence of turbulent solutions to a quantum hydrodynamic (QHD) system, with periodic boundary conditions. A suitable nonlinear change of variables (the Madelung transfor...
The Brauer group, classifying Azumaya algebras up to Morita equivalence, is a fundamental invariant in number theory and algebraic geometry. Given a moduli problem M (e.g. smooth curves of a given gen...
We consider general two-dimensional autonomous velocity fields and prove that their mixing and dissipation features are limited to algebraic rates. As an application, we consider a standard cellular f...
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...
