Date: Friday, 4th March, 2022
Time: 10:30 am to 11:45 am
Venue: Seminar Hall
Twisted conjugacy and orbit decidability in groups
Universitat Politècnica de Catalunya, Spain.
We define the notion of orbit decidability in a general context, and descend to the case of groups to recognise it into several classical algorithmic problems. Then we shall go into the realm of free groups and shall analise this notion there, where it is related to the Whitehead problem (with many variations). After this, we shall enter the negative side finding interesting subgroups which are orbit undecidable. Finally, we shall prove a theorem connecting orbit decidability with the conjugacy problem for extensions of groups, and will derive several (positive and negative) applications to the conjugacy problem for groups.