My email address is edu.berkeley.math@aaron, except that that's not quite it. My office at Berkeley (which I will occupy until mid-August 2016) is 1045 Evans.
Throughout 2012, I was based at the Max Planck Institute for Mathematics in Bonn, Germany. Throughout 2013, I was based at MIT in Cambridge, MA. During the fall 2015 semester, I was based at Montana State University in Bozeman, MT, where I worked with David Ayala.
You can see my c.v. here.
^{*}Last updated 5/19/2016. I am happy to receive any comments, errata, typos, etc.
In my thesis, I develop the theory of model ∞-categories -- that is, of model structures on ∞-categories -- which provides a robust theory of resolutions that is entirely native to the ∞-categorical context. Using this, I generalize Goerss--Hopkins obstruction theory to an arbitrary (presentably symmetric monoidal stable) ∞-category. As a sample application, I use this generalized obstruction theory to construct E_{∞} structures on the motivic Morava E-theory spectra; just as in the classical case, these E_{∞} structures turn out to be essentially unique, and their automorphism groups turn out to be essentially discrete (though they will generally be strictly larger than the usual Morava stabilizer group).
I have also split out the first section of the introductory chapter into an essay called The zen of ∞-categories, which you can see here. This is an introduction to abstract homotopy theory. In the interest of accessibility to a broad mathematical audience, it is centered around the classical theory of abelian categories, chain complexes, derived categories, and derived functors.
The first part of my thesis (regarding model ∞-categories) is assembled from the following papers.
The unoriented cobordism ring is π_{*}(MO)=Z/2[{x_{n}:n≠2^{t}-1}]=Z/2[x_{2},x_{4},x_{5},x_{6},x_{8},x_{9},...].
The complex cobordism ring is π_{*}(MU)=Z[{x_{2n}}]=Z[x_{2},x_{4},x_{6},...].
a/s/l?