In-Person and Online Talk 

Arf rings are algebroid curves whose successive blow-ups satisfy certain special conditions. They are classical objects in singularity theory, having appeared in the works of Arf, Duval, Zariski, Lipman and others. I will describe some recent results concerning module and ideal-theoretic aspects of Arf rings. For instance, they admit  finitely many indecomposable reflexive modules, which correspond precisely to the infinitely near  points. The new results reveal surprising similarities between Arf rings and rational singularities in dimension two, and I will discuss some open questions about such connections.