Research

A broad description of my research interests and a list of my publications and preprints.

Research Interests

I am broadly interested in operator algebras — more specifically C-algebras. My thesis concerns C-algebras arising from partial C-dynamical systems. In particular, I studied the ideal structure of crossed product C-algebras using injective envelope techniques. The rich structure of injective envelopes allows for powerful tools to connect properties of the reduced crossed product such as the intersection property to dynamical properties of the action.

An aspect that has always fascinated me about the field of operator algebras is its connection to the foundations of quantum theory. Throughout my post-graduate studies, I have continued to explore this connection through a pure mathematical lens. For example, I have also been working on projects related to quantum graphs. Quantum graphs arise as a noncommutative generalization of classical graphs in graph theory. They have first been introduced as a generalization of non-confusability graphs in error correction. There are two main approaches to this noncommutative generalization, which have been shown to be equivalent in the past. The first approach involves a quantization of the edge relation and the second is given by a quantiziation of the adjacency matrix. I am mainly interested in finding appropriate generalizations of concepts in graph theory to the theory of quantum graphs.

Preprints

Published articles