Welcome to Niles's webpage!
I am an associate professor in algebraic topology at The Ohio State University. I am a member of the Department of Mathematics, and I teach on the Newark Campus.
Slides from the topology seminar at University of Haifa:
Graded Picard categories and the 2-type of the sphere
Slides from the colloquium at Florida State University:
Algebraic K-theory for 2-categories
Bimonoidal Categories, En-monoidal Categories, and Algebraic K-theory, a three-volume work on bimonoidal and higher ring-like categories. Volumes I and II by Donald Yau, and Volume III jointly written by the two of us.
Update 2022-03-18: More typos fixed; new content about internal hom for M1-modules. See change log for further details.
- 2-Dimensional Category Theory, an elementary text on 2-/bicategories with Donald Yau. Known errata available on our book webpage.
- I wrote a survey article with my coauthors Nick Gurski and Angélica Osorno about our work. It's out in the September 2019 issue of the AMS Notices!
My research interests extend toward both categorical and computational aspects of algebraic topology. Categorical frameworks provide a context in which to develop the "brave new algebra" of structured ring spectra. I'm interested particularly in understanding Picard/Brauer theory and their connections with the Galois theory of ring spectra.
I began interacting with computational aspects of structured ring spectra in joint work with Justin Noel. This work includes computer calculations of power operations and an obstruction spectral sequence for maps of structured ring spectra. Some of my other computational work relates to low-degree Lie algebra cohomology, in joint work with the UGA Algebra Group.
All of my papers, published and preprint, are available on the arXiv. You can also see an overview on my CV (html).
TeachingMy teaching homepage has links to my current courses and a collection of fun topics related to current and previous course material.
MathMeetings.net is a web application for conference announcements. The application lets anyone from the community add conference announcements, storing them in a database and displaying them sorted by date and subject.
Other things I do
Information about some of my other interests (with pictures!) is available in the Etcetera section of this site.
I have a few different open-source side projects that are sometimes useful to others:
- conference-list is the underlying software for MathMeetings.net
- simple-conference is a simple app for hosting conference info and registration
- latex_starter has my latex templates
- refdeps is a tex package to draw a graph of reference dependencies
- Visualization of A(2)