We use the formalism of Quantitative Hydrodynamics to improve the quantitative hydrodynamic limit obtained in Chariker, De Masi, Lebowitz and Presutti (2023) for an interacting particle system inspire...
Variational theories for cohesive fracture models hinge on free discontinuity energies having surface densities that are bounded and concave functions of the jump amplitude. Their phase-field app...
For the hard sphere gas, cumulants have been introduced to encode correlations between particles. In recent years, they have played a central role in the study of kinetic limits, fluctuations, and lar...
Hodge originally formulated his conjecture with integral coefficients. Atiyah and Hirzebruch showed in 1962 that it fails for torsion classes, and later Kollár produced non-torsion counterexamples. Si...
I will discuss a variant of the classical optimal transport dynamical problem, in which the entropy along the curve is minimized additionally to the kinetic energy.This results into a regularizat...
In this talk, I will present recent results on two-dimensional Bose gases with attractive interactions. More precisely, I will discuss the validity of Hartree theory, which states that the ground stat...
I will describe the more recent developments starting from the results contained in two joint works with I. Birindelli and H. Ishii. In [1] we extend to fully nonlinear operators of the we...
Motivated by the study of periodic Hamiltonians enjoying chiral or particle-hole symmetry, like the SSH model or the Kitaev chain, we present a topological study of families of symmetric functions fro...
The Poisson boundary is a measure-theoretic object attached to a group equipped with a probability measure, and is closely related to the notion of harmonic function on the group. In many cases, the g...
We characterize rotationally symmetric solutions to the Serrin problem on ring-shaped domains in ℝn (n ≥ 3). Our proof relies on a comparison geometry argument. In particular, by taking advantage of a...
