Aaron Mazel-Gee

Hello! My name is Aaron. I like to do math. It is my job.

I am currently a Sherman Fairchild Instructor in Mathematics at Caltech. My office is 285 Linde Hall.

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.

My email address is etale.site@aaron, except that you need to swap what comes before and after the "@" symbol.

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


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researches

= undergraduate advisee

[most info]

[least info]

in progress:

forthcoming: forthcame:
  1. Derived Mackey functors and Cpn-equivariant cohomology, with David Ayala and Nick Rozenblyum, 05/06/2021
    arxiv:2105.02456, 82 pages.
    [more info]

  2. A universal characterization of noncommutative motives and secondary algebraic K-theory, with Reuben Stern, 04/08/2021
    arxiv:2104.04021, 80 pages.
    [more info]

  3. Dualizable objects in stratified categories and the 1-dimensional bordism hypothesis for recollements, with Grigory Kondyrev and Jay Shah, 03/29/2021
    arxiv:2103.15785, 61 pages.

  4. Stratified noncommutative geometry, with David Ayala and Nick Rozenblyum, 10/31/2019
    arxiv:1910.14602, 190 pages.
    [more info]

  5. E automorphisms of motivic Morava E-theories, 01/17/2019
    arxiv:1901.05713, 6 pages.

  6. Goerss--Hopkins obstruction theory for ∞-categories, 12/18/2018
    arxiv:1812.07624, 54 pages.

  7. The geometry of the cyclotomic trace, with David Ayala and Nick Rozenblyum, 10/17/2017
    arxiv:1710.06409, 48 pages.
    [more info]

  8. Factorization homology of enriched ∞-categories, with David Ayala and Nick Rozenblyum, 10/17/2017
    arxiv:1710.06414, 68 pages.
    [more info]

  9. A naive approach to genuine G-spectra and cyclotomic spectra, with David Ayala and Nick Rozenblyum, 10/17/2017
    arxiv:1710.06416, 84 pages.

  10. Model ∞-categories III: the fundamental theorem, 10/16/2015
    New York Journal of Mathematics, to appear.
    arxiv:1510.04777, 34 pages.

  11. Model ∞-categories II: Quillen adjunctions, 10/15/2015
    New York Journal of Mathematics, to appear.
    arxiv:1510.04392, 29 pages.

  12. Hammocks and fractions in relative ∞-categories, 10/14/2015
    Journal of Homotopy and Related Structures, 13 (2018), no. 2, 321-383.
    arxiv:1510.03961, 43 pages.

  13. On the Grothendieck construction for ∞-categories, 10/13/2015
    Journal of Pure and Applied Algebra, 223 (2019), no. 11, 4602-4651.
    arxiv:1510.03525, 41 pages.

  14. The universality of the Rezk nerve, 10/12/2015
    Algebraic & Geometric Topology, 19 (2019) no. 7, 3217-3260.
    arxiv:1510.03150, 26 pages.

  15. A user's guide to co/cartesian fibrations, 10/08/2015
    Graduate Journal of Mathematics, 4 (2019), no. 1, 42-53.
    arxiv:1510.02402, 16 pages.

  16. Quillen adjunctions induce adjunctions of quasicategories, 01/13/2015
    New York Journal of Mathematics, 22 (2016), 57-93.
    arxiv:1501.03146, 20 pages.

  17. Model ∞-categories I: some pleasant properties of the ∞-category of simplicial spaces, 12/29/2014
    arxiv:1412.8411, 66 pages.

  18. From fractions to complete Segal spaces, with Zhen Lin Low, 09/29/2014
    Homology, Homotopy and Applications, 17 (2015), no. 1, 321-338.
    arxiv:1409.8192, 21 pages.
    [more info]

  19. A relative Lubin--Tate theorem via meromorphic formal geometry, with Eric Peterson and Nathaniel Stapleton, 08/25/2013
    Algebraic & Geometric Topology, 15 (2015) no. 4, 2239-2268.
    arxiv:1308.5435, 18 pages.

thesis
  1. Goerss--Hopkins obstruction theory via model ∞-categories, 05/13/2016
    545 pages.
    This comprises papers 3, 6, 7, 8, 9, 10, 14, and 15 above, plus an introductory chapter (76 pages).
    [more info]

undergrad researches
  1. A cubical antipodal theorem, with Kyle E. Kinneberg, Tia Sondjaja, and Francis Su, 09/02/2009
    arxiv:0909.0471, 15 pages.
    This is the result of an REU I did in the summer after my sophomore year, supervised by Francis Su.

  2. Maximum volume space quadrilaterals, with Thomas Banchoff and Nicholas Haber, 08/02/2006
    Expeditions in Mathematics, 2 (2011), 175-198.
    23 pages.
    This is the result of a summer research project I did in the summer after my freshman year, supervised by Thomas Banchoff. If it counts, this gives me an Erdős number of 4. (And if we somehow make a movie adaptation, I'll have a Bacon number of 4 too.)

book
  1. An invitation to higher algebra (in progress, see here for more info)

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. You can see the syllabus here.

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,...].

a/s/l?

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