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.
♣ = student advisee
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.
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,...].
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.