I am a Sherman Fairchild Instructor in Mathematics at Caltech. My office is 374 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".

I am the organizer of Caltech's geometry & topology seminar. All are welcome to join.

cv talks expository writing teaching teaching materials conferences double conferences service PR livetex xkcd

^{♣} = student advisee

- A braided (∞,2)-category from Soergel bimodules,
*with Yu Leon Liu*^{♣}*, David Reutter, Catharina Stroppel, and Paul Wedrich*

To appear.Here is a video of a talk about this material (starting a minute or two in, due to a technical glitch). Updated slides are here -- those contain a (very sketchy) sketch of the proof, which I didn't discuss in the recorded talk.

And here is a video of Catharina's 2022 ICM plenary address (whose accompanying survey article is here). She gives a broad overview of TQFT and categorification, and ends by putting our main theorem into that context.

- Perverse schobers and 3d mirror symmetry,
*with Benjamin Gammage and Justin Hilburn*, 02/14/2022

arxiv:2202.06833, 43 pages.

[more info] - Derived Mackey functors and C
_{pn}-equivariant cohomology,*with David Ayala and Nick Rozenblyum*, 05/06/2021

arxiv:2105.02456, 84 pages.

[more info] - A universal characterization of noncommutative motives and secondary algebraic K-theory,
*with Reuben Stern*^{♣}, 04/08/2021

arxiv:2104.04021, 80 pages.

[more info] - 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. - Stratified noncommutative geometry,
*with David Ayala and Nick Rozenblyum*, 10/31/2019

*Memoirs of the AMS*, to appear.

arxiv:1910.14602, 236 pages.

[more info] - E
_{∞}automorphisms of motivic Morava E-theories, 01/17/2019

arxiv:1901.05713, 6 pages. - Goerss--Hopkins obstruction theory for ∞-categories,
12/18/2018

arxiv:1812.07624, 54 pages. - The geometry of the cyclotomic trace,
*with David Ayala and Nick Rozenblyum*, 10/17/2017

arxiv:1710.06409, 48 pages.

[more info] - Factorization homology of enriched ∞-categories,
*with David Ayala and Nick Rozenblyum*, 10/17/2017

arxiv:1710.06414, 68 pages.

[more info] - A naive approach to genuine G-spectra and cyclotomic spectra,
*with David Ayala and Nick Rozenblyum*, 10/17/2017

arxiv:1710.06416, 84 pages. - Model ∞-categories III: the fundamental theorem,
10/16/2015

*New York Journal of Mathematics*, 27 (2021), 551-599.

arxiv:1510.04777, 34 pages. - Model ∞-categories II: Quillen adjunctions,
10/15/2015

*New York Journal of Mathematics*, 27 (2021), 508-550.

arxiv:1510.04392, 29 pages. - 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. - 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. - The universality of the Rezk nerve,
10/12/2015

*Algebraic & Geometric Topology*, 19 (2019) no. 7, 3217-3260.

arxiv:1510.03150, 26 pages. - 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. - Quillen adjunctions induce adjunctions of quasicategories,
01/13/2015

*New York Journal of Mathematics*, 22 (2016), 57-93.

arxiv:1501.03146, 20 pages. - Model ∞-categories I: some pleasant properties of the ∞-category of simplicial spaces,
12/29/2014

arxiv:1412.8411, 66 pages. - 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] - 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.

- 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]

- 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. - 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.)

- 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[{x_{n}:n≠2^{t}-1}]=Z/2[x_{2},x_{4},x_{5},x_{6},x_{8},x_{9},...]*.

The

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.