Model theory has a long history of significant interaction with, and applications to, algebra, geometry, and number theory. One of the main sources of this interaction has been the study of fields equipped with distinguished operators, in particular derivations (differential algebra) and automorphisms (difference algebra). This has lead to major applications of model-theoretic techniques to differential-algebraic geometry and algebraic dynamics – which can be seen as the geometric avatars of differential and difference algebra, respectively – beginning in the early Nineties. However, in the last five years, there has been a shift in the nature of these interactions, based on the use of specialised finite rank techniques in model theory, and leading to a rapid development of breakthrough applications.

 

The purpose of this workshop is two-fold. The first goal is to focus on these two related areas of model-theoretic application, and to facilitate a sharing of techniques being used. The second is to attempt to provide a unified understanding of results in algebraic dynamics and differential-algebraic geometry, and, in particular, to ask whether recent advances in the latter coming from the use of binding groups and other key model-theoretic techniques have natural analogues in algebraic dynamics.