Gianluca Paolini,University of Torino

Since the work of Sela, and Kharlampovich & Myasnikov on Tarski’s problem for non-abelian free groups, the model theoretic analysis of classes of groups arising from combinatorial and geometric group theory has seen crucial advancements. The work that I am going to present is in this tradition, and it presents a model-theoretic study of an important class of finitely presented groups known as Coxeter groups. Specifically, I will present an overview of my paper joint with B. Mühlherr and S. Shelah on the first-order model theory of Coxeter groups (J. Algebra 595 (2022), 297-346), and then talk about recent developments on the same subject in an ongoing joint project with R. Sklinos.