Aaron Mazel-Gee

My name is Aaron. I like to do math. It is my job. I'm in my third year of grad school at UC Berkeley. I like algebraic topology. My advisor is Peter Teichner. I work in chromatic homotopy theory. It is very nice.

My email address is noraa@math.berkeley.edu, except that that's not quite it. My office at Berkeley is 1044 Evans. Throughout 2012, I was based at the Max Planck Institute for Mathematics in Bonn, Germany. I am currently studying at MIT, where my office is 2-094.

My current projects include...

...a hunt for manifestations of certain properties of p-adic modular forms in tmf. The idea is that p-adic modular forms, despite being inherently K(1)-local, should nevertheless be able to detect the existence of the K(2)-local world. You can find a very rough sketch here (the asterisked item), and here is a fun (although by now somewhat outdated) little flowchart that I've been keeping to help me organize how all the various concepts relate to each other.
...a motivic Goerss-Hopkins obstruction theory (with Markus Spitzweck).
...a categorical framework in which to quantify the extent to which some category captures "all the structure" on the image of some topology-to-algebra functor, especially for algebras over a monad. (For instance, the p-adic K-theory of an E_∞-ring spectrum is naturally a θ-algebra. Is this the best possible characterization? If so, why?)

The latest (and perhaps final) version of 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.

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The unoriented cobordism ring is π_{_*}(MO)=Z/2[{x_n:n≠2^t-1}]=Z/2[x₂,x₄,x₅,x₆,x₈,x₉,...].
The complex cobordism ring is π_{_*}(MU)=Z[{x_2n}]=Z[x₂,x₄,x₆,...].