Welcome to Niles's webpage!
- Slides for my recent talk at Reed College about visualizing the Hopf fibration.
- 2-Dimensional Category Theory, an elementary text on 2-/bicategories with Donald Yau.
- Slides for my recent talk at Case Western about algebraic K-theory for 2-categories.
- 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.
Here is the schedule for our Homotopy Theory Seminar. The seminar meets on Thursdays at 11:30 in MW 154.
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'm sometimes active on Twitter @NilesTopologist.
When I see something to contribute to Wikipedia, I do it.
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)