Walter Boscheri va passer l'année 2023 à l'IMB il va présenter ses travaux et sujets sur lesquels il peut être un partenaire privilégié.
In this talk I briefly introduce myself by presenting the main lines of research which I am currently working on. The first part of the talk is devoted to the problems tackled so far, namely high order numerical schemes on moving meshes, semi-implicit asymptotic preserving schemes, semi-Lagrangian methods and numerical algorithms for the solution of kinetic equations in the context of rarefied gas dynamics as well as epidemic spreading in social dynamics. The second part of this presentation will provide an outlook to future research topics to be carried out mainly in Bordeaux during my visiting period in the next year. Lagrangian schemes on curvilinear meshes, structure preserving methods for plasma flows and hyperelasticity, and entropy stable algorithms are some of the foregoing research activities.