About Me

I am a Visiting Assistant Professor of Mathematics and Computer Science at Davidson College. My main areas of interest are (spectral) graph theory, operator theory, and mathematical physics. I am especially interested in interdisciplinary questions which use tools from these fields in unexpected ways. More broadly, I seek to understand the interplay between various continuous and discrete structures. I am also interested in the roles of diversity and inclusivity mathematics, and in the development of teaching practices which better serve students from underserved groups.

COLLABORATORS

RESEARCH

The GKSL Master Equation

Much of my current research revolves around the GKSL master equation, the most general equation for describing Markovian and time-homogenous evolution of a quantum system. I am particularly interested in the connections this equation has to graph theory and in generalizing this equation to infinite dimensions without boundedness assumptions.

George Androulakis

University of South Carolina

Matthew Ziemke

Drexel University

The Dark Web

I am interested in the use of quantum techniques to describe the structure of internet black markets. In particular, my collaborators and I seek to determine the survival mechanisms which allow these marketplaces to proliferate despite the efforts of law enforcement.

Digraph Spectra

Classifying cospectral graphs is an interesting open problem for which much work has been done in recent years. Directed graphs are far, far less likely to be determined by their spectrum, so we propose an alternative `spectrum' as a way to classify graphs in the directed case. The first set of classifications can be found here, and a second paper in is preparation.

Felipe Thomaz

University of Oxford

Gregory Clark

University of Oxford

Thomas Cameron

Davidson College

Michael Robertson 

Davidson College '20