expository writing

Caveat lector: let the reader beware. The resources below are byproducts of my various efforts to learn various things over the years -- often through speaking about them. I certainly can't vouch for their accuracy. Nevertheless, I'm keeping them available here, in case others might find them useful.

Beyond being organized by topic, these are in no particular order.

If you'd like, you can show all abstracts or hide all abstracts.

chromatic homotopy theory

You could've invented tmf. These are my slides from the "distinguished graduate student lecture" that I delivered at USTARS in spring 2013. [abstract]

Construction of TMF (or see the notes in context, pp. 16-27). This is from the Uni-Bonn student doctoral seminar in fall 2012 on TMF. The first section ("You could've invented tmf") puts forward a perspective which I think is quite natural, but which I haven't seen it anywhere in the literature (at least not this explicitly). Of course, certainly it's been familiar to the architects of tmf since the beginning.

Dieudonné modules and the classification of formal groups. This is from a talk in the xkcd seminar in fall 2011. [abstract]

The chromatic tower. These are some notes from a talk I gave in the MIT Juvitop/pre-Talbot seminar on the chromatic tower. There is a video of this talk here. I never wrote this into the notes, but there I managed to wrap things up with a huge diagram of interrelated spectral sequences. [abstract]

Algebraic cobordism, algebraic orientations, and motivic Landweber exactness. These are the handwritten notes from my (post-Talbot) talk in the MSRI pre-Talbot seminar of spring 2014. [abstract]

π*LE(1)S for p≠2. This is a short note detailing the computation of the homotopy groups of the E(1)-local sphere at odd primes, transcribed from a conversation with Justin Noel (although all mistakes are certainly my own).

A Survey of Lurie's "A Survey of Elliptic Cohomology". This is unfinished (I never fleshed out the flowchart of the proof of the main theorem). [abstract]

p-adic modular forms and Dieudonné crystals in stable homotopy theory. This is a poster for GAeL XX. You can see that I was rather pressed for space. The bibliography is here.

black-and-white homotopy theory

The zen of ∞-categories. This is an expository essay extracted from the introductory chapter of my thesis. [abstract]

Model categories for algebraists, or: What's really going on with injective and projective resolutions, anyways?. This is from a talk in Berkeley's toolbox seminar in fall 2012. [abstract]

An introduction to spectra. This is from a talk I gave in the GRASP (Geometry, Representation theory, And Some Physics) seminar in spring 2011. [abstract]

From Morse theory to Bott periodicity. This is from a sequence of talks in the xkcd seminar, two in spring 2011 and one in fall 2011. [abstracts]

Higher cohomology operations. This is from a talk in the xkcd seminar in fall 2010. The nature of the material makes it nearly impossible to tex up in as clear (if not clean) a way as handwriting with colored pens, so this is a 7.87MB scan. Consider yourself warned. [abstract]

The Steenrod algebra and its applications, part 1 and part 2. These are from a sequence of three talks in the xkcd seminar in fall 2010, but notes from the third would've been lifted directly from Chapter 12 of Mosher and Tangora (on computing homotopy groups of spheres), so I didn't bother. Also, here's a table of the first few monomials in the Steenrod algebra organized by degree and excess. An Adem relations calculator is available here. [abstracts]

Homotopy (co)limits and n-excisive functors (or see the notes in context, pp. 8-20). This is from the Uni-Bonn Arbeitsgemeinshaft in spring 2012 on Goodwillie calculus.

Fibered categories (or see the notes in context, pp. 6-10). This is from a talk in Martin Olsson's seminar on stacks in fall 2011.

Semidirect products are homotopy quotients. This is a short (and extremely outdated) note in which I tried to sort out a hierarchy of various possible interactions between a group and a category. [abstract]

not homotopy theory

Category O, Soergel bimodules, and the Kazhdan--Lusztig conjectures. These are slides from a talk given in a learning seminar on Soergel bimodules.

Homological integration, Feynman diagrams, and the divergence complex. These are notes from a pair of talks given jointly with Eugene Rabinovich in a learning seminar on factorization algebras.

Introduction to supermanifolds. This is from a talk I gave in the 80s math for 80s babies (a/k/a Witten in the 80s) seminar. These notes were texed by Theo Johnson-Freyd. Someday I may add a bit that I skipped during the actual talk on Harish-Chandra pairs.