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 work is partially supported by NSF grant DMS-2105031 (Factorization homology and low-dimensional topology).

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]

  1. Perverse schobers and 3d mirror symmetry, with Benjamin Gammage and Justin Hilburn, 02/14/2022
    arxiv:2202.06833, 43 pages.
    [more info]

  2. Derived Mackey functors and Cpn-equivariant cohomology, with David Ayala and Nick Rozenblyum, 05/06/2021
    arxiv:2105.02456, 83 pages.
    [more info]

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

  4. 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.

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

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

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

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

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

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

  11. Model ∞-categories III: the fundamental theorem, 10/16/2015
    New York Journal of Mathematics, 27 (2021), 551-599.
    arxiv:1510.04777, 34 pages.

  12. Model ∞-categories II: Quillen adjunctions, 10/15/2015
    New York Journal of Mathematics, 27 (2021), 508-550.
    arxiv:1510.04392, 29 pages.

  13. 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.

  14. 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.

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

  16. 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.

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

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

  19. 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]

  20. 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)
    Contracted to be published in the Cambridge University Press series Studies in Advanced Mathematics.

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.