Niles Johnson

I am a postdoc in algebraic topology at the University of Georgia.

In Fall 2012 I will be starting as an assistant professor at Ohio State Newark!

Latest additions:

• In the obstruction theory project with Justin Noel, we now have a working draft for the web: Lifting homotopy T-algebra maps to strict maps.
• An illustrated construction of spectral sequences.
• Visualizing Seven-Manifolds animation project.
• ArXiv preprint on Stable One-Types; joint with Angélica Osorno.

You may also be looking for information about things I help organize:

• The UGA Algebra Seminar
• The VIGRE Graduate Seminar
• AlgTop-Conf, a conference announcement list for topologists

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 includes some computer calculations of power operations and (forthcoming) 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).

In the Spring of 2012, I am teaching our graduate homological algebra course.

During the Fall of 2011 I taught Math 2500, Multivariable Calculus.

In the Spring of 2011, I taught two elementary geometry courses through our department's Mathematicians Educating Future Teachers initiative. Before that I taught point-set topology in the Fall of 2011, and calculus courses at UGA and U. Chicago.

Here you can find a lists of patches I've worked on and patches I've reviewed from the Sage development site trac.sagemath.org.

Here's an overview of my activity on the Sage support website ask.sagemath.org.

I've started compiling a collection of my personal latex tips.

I use Dropbox to store some of my files online. If you use this link to sign up, we both get a storage bonus!

Information about some of my other interests (with pictures!) is available in the personal pictures & projects section of this site.