Speaker:
Oleg Bogopolski (University of Szczecin)

Title:
Acylindrically hyperbolic groups: equations and elementary equivalence

Abstract:
The class of  acylindrically hyperbolic groups (AH-groups) is the 
subject of intensive investigations in the modern geometric group 
theory. It  contains  all relatively hyperbolic groups, most mapping 
class groups, all groups of deficiency at least two, and many other 
interesting groups. In the first part of my talk, I will present my 
recent results about solutions of certain equations in AH-groups and 
about  algebraic and verbal closedness of AH-groups in overgroups. 
In the second part I will survey some known results about elementary 
equivalence in the classes of nilpotent, virtually free, AH-groups, 
and raise some questions.