Free- and Amalgamated Products in Group Rings
Talk by Doryan Temmerman (UHasselt), at the Antwerp Algebra Colloquium on March 25, 2022.
In this talk, we will bridge the gap between the theory of Group Rings and Geometric Group Theory. We will briefly introduce a couple of conjectures that have been guiding the research in Group Rings over the last couple of decades. Using these conjectures as a motivation we will discuss how the amalgamated product of groups, a construction naturally appearing in Geometric Group Theory, warrants consideration within this domain. In doing so, my goal will be to provide you with an idea of the types of questions, and directions for solutions, that come up within the research field of Group Rings. Skipping the technical details, we will only hit the highlights of this beautiful interplay while strolling next to Bass-Serre Theory, Orders and Linear Groups.