Aaron Mazel-Gee

My name is Aaron. I like to do math. It is my job. I recently finished grad school at UC Berkeley. I am currently a Research Assistant Professor at USC.

My research centers around factorization homology, especially as it relates to (i) quantum invariants in low-dimensional topology, and (ii) algebraic K-theory, elliptic cohomology, and chromatic homotopy theory.
Other mathematical interests include: Fukaya categories, arboreal singularities, and microlocal sheaves; shifted symplectic & Poisson structures; equivariant and motivic homotopy theory.

You can see my c.v. here.

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

My office at USC is KAP 438D.

My last name is pronounced "may-zell jee".

I am an active proponent of double conferences, a new eco-friendly conference format whose purpose is to reduce long-distance travel while still fostering long-distance interactions. Events take place in two different locations connected by live video stream. The first double conference was held in August 2018, entitled Higher algebra and mathematical physics and co-hosted by the Perimeter Institute for Mathematical Physics (Waterloo, Canada) and the Max Planck Institute for Mathematics (Bonn, Germany); you can see the conference websites here and here. Organization of a second double conference is underway. If you might be interested in running a double conference, please feel free to get in touch with me, and also read our (the organizers') short write-up of our experience on page 32 of this issue of the London Mathematical Society newsletter.
The geometry of the cyclotomic trace: In collaboration with David Ayala and Nick Rozenblyum, I have recently developed a new construction of topological cyclic homology (TC) that accommodates a precise interpretation at the level of derived algebraic geometry of the cyclotomic trace K → TC from algebraic K-theory. It uses nothing but the geometry of 1-manifolds (via factorization homology) and universal properties (coming from Goodwillie calculus). The project comprises three papers:
  1. A naive approach to genuine G-spectra and cyclotomic spectra,
  2. Factorization homology of enriched ∞-categories, and
  3. The geometry of the cyclotomic trace.
The main results are contained in paper 3, which is intended to be accessible to a relatively broad audience. (In particular, it can be read entirely independently of papers 1 and 2.)

Here is a short description of the project which is intended to be readable by a non-mathematical audience (though it almost surely isn't wholly so).

[show additional resources]

My PhD thesis is entitled Goerss--Hopkins obstruction theory via model ∞-categories. You can see it here.* You can also see the movie adaptation here. [show more]

*Last updated 4/8/2019. 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.

I have written the following other research papers (aside from the 14 referenced above (click "show more" to see those related to my thesis)).
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, Antieau, Ayala, Ben-Zvi, Carchedi, Corwin, Duhl-Coughlin, Farris, Gepner, Hansen, Jordan, Li-Bland, Nadler, Orman, Penneys, Roberts, Spivak, Treumann, White.

writing       talks       teaching       conferences       service       PR       xkcd seminar       livetex

The unoriented cobordism ring is π*(MO)=Z/2[{xn:n≠2t-1}]=Z/2[x2,x4,x5,x6,x8,x9,...].
The complex cobordism ring is π*(MU)=Z[{x2n}]=Z[x2,x4,x6,...].