From interacting particle systems to kinetic equations

In multiscale modeling hierarchy, the Boltzmann and related kinetic equations serve as a building block that bridges microscopic Newtonian mechanics and macroscopic continuum mechanics. In this short course, I will start with a brief introduction of basic kinetic equations, and then discuss various numerical aspects of efficiently solving these equations, including fast algorithms for collision operators, asymptotic-preserving schemes for multiscale problems. I will also cover some recent development on uncertainty quantification for kinetic equations.