Abstract: Groupoids are a natural generalization of groups and with the help of Jean Renault, Dana Williams, and several others, have given operator algebraists more tools to generate examples of operator algebras in different contexts. In this talk, we will define and explore examples of groupoids (in mostly the general setting, sorry smooth fans). After exploring groupoid world, we will define and build a certain type of operator algebra from topological groupoids and discuss the issues that arise from even attempting to do so. We will then discuss a nice type of groupoid built from directed graphs along with (briefly) defining a generalization of directed graphs called quantum graphs. Finishing up, we will state the open problem of connecting groupoids to quantum graphs and what implications could occur in the event of a positive answer.
