Classification is a common theme in mathematics, encompassing the idea that quite complicated objects are completely determined by some simpler objects associated to them, called invariants. To a C*-algebra, one can associate a pair of abelian groups (its K-theory, generalising the topological K-theory) and a Choquet simplex (its space of traces). This so-called Elliott invariant cannot distinguish all C*-algebras, but due to remarkable work by many researchers over the last three decades, it completely determines simple, separable, nuclear C*-algebras which have enough regularity (technically, they tensorially absorb an infinite-dimensional version of the complex numbers called the Jiang-Su algebra and satisfy the universal coefficient theorem of Rosenberg and Schochet).
My research interests span across operator algebras and their dynamics. I am interested in using tools from the classification theory of C*-algebras to study inclusions of C*-algebras and develop regularity properties for them. Another important direction of my research is the study of classical and quantum symmetries of C*-algebras. More precisely, I am interested in studying actions of the real numbers on C*-algebras via their induced KMS states as well as in the classification of actions of tensor categories on C*-algebras in the spirit of subfactor theory. For a glimpse into this last topic, you can have a look at this poster presenting joint work with Sergio Giron Pacheco.