Model theory and the Lazard Correspondence

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.

group theorylogicnumber theory

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic