Speaker: 
Daniel Max Hoffmann (University of Warsaw)

Title: 
Structures with finite group action

Abstract:
I will present results from my joint project with Piotr Kowalski. 
In my talk, I will outline the general results, leaving interesting 
examples and applications to the speaker of the next talk. Take a 
monster model M of a stable theory and a group G. Consider the family 
of all substructures of M equipped with a group action (by automorphisms) 
of G. The question is whether the sub-family of existentially closed 
substructures with a group action of G forms an elementary class. In 
other words, whether we can find an axiomatization of the model companion 
of substructures with a group action of G. We will analyze the situation 
for finite G and express the problem in terms involving only the invariants 
of the group action. It is somehow surprising how important the notion of 
a PAC substructure is in this scenario.