[Turkmath:1082] Model Theory Day at IMBM

[Ozlem Beyarslan]

Dear All,
The first of  "IMBM Model Theory Meetings" will be on Friday, March 4. The
first talk starts at 11:30
The full information is below and the poster is attached.
We thank IMBM for their hospitality,

Özlem Beyarslan


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IMBM Model Theory Meetings

Friday, March 4

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.

-- 
Özlem Beyarslan

Bogazici Universitesi Matematik Bolumu
Bebek, Istanbul 34342
Tel: 90 212 359 6535
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