During the workshop “Kinetic Limits and Probability” (La Sapienza, Rome, June
9–13, 2025), a round table took place, during which some recent and important
developments of kinetic theory were presented and discussed. The present article is a
description of this round table. After a brief overview of the state of art in kinetic
theory, several open questions are presented, regarding on the one hand the
derivation of the Boltzmann equation from Hamiltonian particle systems in the low
density limit (Lanford’s theorem), and on the other hand the problems of
hydrodynamic limits, that is, the derivation of the fluid dynamics equations from the
Boltzmann equation. We also report on the presentation and discussion about the
recent results of Deng, Hani and Ma on the long-time derivation of the Boltzmann
equation, which Zaher Hani himself presented during the round table of the
workshop.
