My email address is etale.site@aaron, except that that's not quite it.

You can see my c.v. here.

My current research interests are: factorization homology, derived algebraic geometry, and algebraic K-theory; quantum field theory and shifted geometric structures; higher category theory, abstract homotopy theory, and their applications to equivariant and motivic homotopy theory; chromatic homotopy theory and its interactions with number theory; the human condition.

My PhD thesis is entitled

^{*}Last updated 10/17/2016. I am happy to receive any comments, errata, typos, etc.

I have also split out the first section of the introductory chapter of my thesis 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 Adem relations calculator is here -- brought to you, as always, by the wizardry of the kruckmachine.

I passed my qualifying exam on Friday, May 13, 2011.

Here is a diagram from a class I taught, which attempts to summarize the relationship between relative categories, model categories, quasicategories, and ∞-categories.

The DavidRoll: Alper, Ayala, Ben-Zvi, Carchedi, Corwin, Duhl-Coughlin, Gepner, Hansen, Jordan, Li-Bland, Nadler, Orman, Penneys, Roberts, Spivak, White.

writing talks teaching conferences service PR xkcd seminar livetex

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

a/s/l?