turkmath.org

11:30-12:30 Özlem Beyarslan (Boğaziçi Üniversitesi)
Title: Geometric Representation in the Theory of Pseudo-Finite Fields
Abstract: We will discuss the concept of geometric representation. We will show that any finite group which is geometrically represented in a pseudo-finite field must be abelian. This result also generalises to bounded PAC fields. This is joint work with Zoe Chatzidakis.

14:00-15:00 Piotr Kowalski (Uniwersytet Wrocławski)
Title: Existentially closed fields with finite group actions
Abstract: This is joint work with (my PhD student) Daniel Hoffmann. We study Galois field extensions with a fixed finite Galois group G. We call such an extension a G-transformal field. We give geometric axioms of the theory of existentially closed G-transformal fields and call the resulting theory G-TCF. Using these axioms, we show that the underlying field of any model of G-TCF is a pseudo-algebraically closed field (abbreviated PAC). We describe purely algebraically constant fields of models of G-TCF: they are perfect PAC fields satisfying an extra G-closedness condition. This condition implies that the underlying PAC field is bounded, hence applying the known results about such PAC fields we conclude that the theory G-TCF is supersimple.

15:30-16:30 Ayhan Günaydın (Mimar Sinan Güzel Sanatlar Üniversitesi)
Title: Topological Study of Pairs of Algebraically Closed Fields

Abstract: Model theoretic study of pairs of algebraically closed fields goes back to Keisler, who proved a completeness result and a quantifier elimination result. Since then there has been quite a bit of work on the subject of expansions of fields by certain subsets. In this talk, I will propose a topological study of pairs of algebraically closed fields. The topology I will introduce is strictly between the Zariski and Kolchin topologies. I will illustrate some results on the interaction of this topology and model theoretic concepts.

ozlem.beyarslan@boun.edu.tr