Decision problems in groups and extensions

Combinatorial group theory is the study of free groups and how groups can be given as a presentation based on generators and relations. There are three famous problems, namely the Word Problem, Conjugacy Problem and Isomorphism Problem, which were first posed by Dehn and have been studied for over a century. In general, it is not possible to solve these problems, but often nice solutions to these problems occur naturally in certain groups.

Among such groups are free groups and free abelian groups. In more recent years, mathematicians have also studied partially commutative groups - also known as right angled Artin groups (RAAG) - which lie somewhere in between free groups and free abelian groups. The Word, Conjugacy and Isomorphism problems are known in RAAGs, but when this is moved to virtually free RAAGs, almost nothing is known. In my research I aim to understand more about the automorphism groups of virtually free RAAGs by working on the conjugacy problem, using a combination of algebraic, combinatorial and geometric methods.