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.

You can find out more about my research on my CV.

Creative Commons License

The pages of nilesjohnson.net are licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.