Welcome to Niles's research page.
My research applies categorical algebra to questions in stable homotopy theory. I am interested in concrete, calculational results, but I often work in abstract theory to develop computational tools. Thus my work bridges between abstract category theory and computations in homotopy theory. I am most motivated by questions about Brauer groups of commutative ring spectra, but I take a broad perspective and my work addresses a range of topics loosely related to Brauer theory.
My core research program uses symmetric monoidal algebra to model stable homotopy theory. This program is a long-term collaboration between myself, Nick Gurski, and Angélica Osorno. Our results have a combination of general theory---such as strictification via abstract 2-monad theory---and concrete results---such as categorical formulas for low-dimensional stable Postnikov invariants.
I've been involved with two other short-term projects; these have the same mix of abstract theory and computational answers, although they are less categorical in nature. In both, my contributions included non-trivial software for automated calculations. That work requires expressing the relevant theory in the most concrete possible terms.