Vincent Villalobos

Many systems within quantum mechanics are modeled by operator algebras. Given some system of observables, we can form the corresponding C*-algebra, where each observable is exhibited by an operator from that C*-algebra. Even further, we can recognize these C*-algebras as C*-algebras of algebraic objects and apply algebraic techniques to investigate them.My research focuses on groupoid C*-algebras. Groupoids serve to directly generalize groups. Many well known C*-algebras arise as groupoid C*-algebras, giving us an opportunity to apply groupoid techniques to obtain results. Currently, I am studying Lie groupoid C*-algebras, which are groupoid C*-algebras with a smooth structure on the groupoid itself.