Model theory of group actions on fields

Abstract: For a fixed group G, we study the model theory of actions of G by field automorphisms. The main question here is to characterize the class of groups G for which the theory of such actions has a model companion (a first-order theory of "large" actions). In my talk, I will discuss several classes of groups G in this context. The case of finite groups is joint work with Daniel Hoffmann ("Existentially closed fields with finite group actions", Journal of Mathematical Logic, (1) 18 (2018), 1850003). The case of finitely generated virtually free groups is joint work with Özlem Beyarslan ("Model theory of fields with virtually free group actions", Proc. London Math. Soc., (2) 118 (2019), 221-256). The case of commutative torsion groups is joint work with Özlem Beyarslan ("Model theory of Galois actions of torsion Abelian groups", arXiv:2003.02329).

dynamical systems

Audience: researchers in the topic

BIRS workshop: Algebraic Dynamics and its Connections to Difference and Differential Equations

Series comments: The field of algebraic dynamics has emerged over the past two decades at the confluence of algebraic geometry, discrete dynamical systems, and diophantine geometry. In recent work, striking connections have been observed between algebraic dynamics and much older theories of difference and differential equations. This meeting brings together mathematicians with expertise in such diverse fields as ring theory, complex dynamics, differential and difference algebra, combinatorics and algebraic geometry. New work towards the dynamical Mordell-Lang and dense orbit conjectures as well as theorems on hypertranscendence and functional independence proven by connecting difference Galois theory, algebraic dynamics and other algebraic approaches to the study offunctional equations will be presented at this meeting.