## Research and Teaching interests

#### Research Interests

My research interests are in operator algebras. I am particularly interested in the representation theory of groupoid C*-algebras and algebras associated with labeled graphs.

Groupoids are versatile objects. They generalize dynamical systems, directed graphs, and even equivalence relations in the sense that each of these objects has an associated groupoid whose C*-algebra is algebraically identical to the usual C*-algebra associated with it. In this way, groupoids give us another angle from which to study these objects.

Due to a famous theorem attributed to Gelfand, Naimark, and Segal, called the GNS Theorem, every C*-algebra can be represented as a concrete algebra of continuous operators on a Hilbert space. Groupoid C*-algebras are built from groupoids, so can we describe specific representations of the groupoid C*-algebra in terms of the groupoid? This is a typical question that I am interested in in my research.

#### Teaching

I love teaching and believe it is an important part of my fabric as an academic. I believe that education can transform lives. It is our most powerful weapon against poverty and social injustice.

My teaching philosophy in a nutshell is to train confident thinkers, able to think analytically about problems both inside and outside of mathematics.

I have taught a broad spectrum of courses in various countries. Particular courses that I loved teaching are multivariable calculus, real analysis, and measure theory. For more, see my webiste.

Personal website: https://danielvanwyk.com/