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.

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".

My current research interests are: factorization homology, derived algebraic geometry, and algebraic K-theory; Fukaya categories, arboreal singularities, and microlocal sheaves; duality phenomena in quantum field theory via factorization homology; quantum field theory and shifted symplectic/Poisson 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.
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 2/19/2018. 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 12 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.

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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,...].