Title: Model theory and the Lazard Correspondence
Speaker: Nick Ramsey (University of Notre Dame)
Abstract: The Lazard Correspondence is a characteristic p analogue of the correspondence between nilpotent Lie groups and Lie algebras, associating to every nilpotent group of exponent p and nilpotence class c a Lie algebra over F_p with the same nilpotence class (assuming c < p). We will describe the role that this translation between nilpotent group theory and linear algebra has played in an emerging program to understand the first order properties of random nilpotent groups. In this talk, we will focus on connections to neostability theory, highlighting the way that nilpotent groups furnish natural algebraic structures in surprising parts of the SOP_n and n-dependence hierarchies. This is joint work with Christian d'Elbée, Isabel Müller, and Daoud Siniora.
