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Model theory of group actions on fields

Banff International Research Station for Mathematical Innovation and Discovery

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 à zlem 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 à zlem Beyarslan ("Model theory of Galois actions of torsion Abelian groups", arXiv:2003.02329).

Mathematics; Dynamical systems and ergodic theory; Difference and functional equations; Dynamical systems

video/mp4

Author affiliation: Uniwersytet Wrocławski

2021-05-12

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/78281

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/