In 2017 Lucio Galeati understood that a suitable scaling limit
of certain hyperbolic PDEs with noise may lead to deterministic
parabolic equations. Since then, in collaboration with Lucio and
Dejun Luo, we have understood the phenomenon from several...
We consider a class of interacting particle systems with two
types, A and B which perform independent random walks at different
speeds. Type A particles turn into type B when they meet another
type B particle. This class of systems includes models...
Our study is motivated by earlier results about nodal count of
Laplacian eigenfunctions on manifolds and graphs that share the
same flavor: a normalized nodal count is equal to the Morse index
of a certain energy functional at the critical point...
We consider systems of NN particles interacting
through a repulsive potential in the Gross-Pitaevskii regime. We
prove complete Bose-Einstein condensation and we determine the form
of the low-energy spectrum, in the limit of large NN. Our
The rigorous calculation of the ground state energy of dilute
Bose gases has been a challenging problem since the 1950s. In
particular, it is of interest to understand the extent to which the
Bogoliubov pairing theory correctly describes the ground...
The Stefan problem, dating back to the XIX century, aims to
describe the evolution of a solid-liquid interface, typically a
block of ice melting in water. A celebrated work of Luis Caffarelli
from the 1970's established that the ice-water interface...