While I dish out plenty of finance-related snark on Twitter, I've also started a blog to cover topics in finance, economics, and beyond in a slightly more serious, in-depth manner. Check out The Market Completionist!
I am a strong supporter of walkable, people-centric urbanism, and a proud foot soldier in the War on Cars. I occasionally blog my urbanist dreams at Let the Midway Bloom.
In a previous life, I was a mathematician. While I'm no longer pursuing mathematics as a vocation, you can still occasionally find me on Math Overflow.
- A double construction for pointed Lie 2-algebras (PhD thesis)
We define a double construction for a certain class of Lie 2-algebras, which provides a pseudofunctor to the 2-category of pointed Manin pairs. We show that this pseudofunctor is essentially surjective, and we expect that it is an equivalence.
- Extensions of groups by braided 2-groups
- We classify extensions of a group G by a braided 2-group B as defined by Drinfeld, Gelaki, Nikshych, and Ostrik. We describe such extensions as homotopy classes of maps from the classifying space of G to the classifying space of the 3-group of braided B-bitorsors. The Postnikov system of the latter space contains a generalization of the classical Pontryagin square to the setting of local coefficients, which has been previously discussed by Baues and more recently, in a setting close to ours, by Etingof, Nikshych, and Ostrik. We give an explicit cochain-level description of this Pontryagin square for group cohomology.
- Spectral Theory
- Notes from lectures given in an undergraduate course on functional analysis in 2010 at the University of Chicago.
Representations of the Symmetric Groups
- Notes from lectures given in an undergraduate course on representation theory in 2009 at the University of Chicago.
- Étale Cohomology Mini-Seminar
- In the fall of 2008, I ran a learning seminar on étale cohomology. We primarily followed James Milne's Lectures on Etale Cohomology, but these notes from the early part of the seminar provide additional background.
- Representation Theory, Symmetry, and Quantum Mechanics
- A talk given to undergraduates at the 2008 University of Chicago VIGRE REU. (Warning: There are several errors in here that I've not gotten around to fixing. Caveat lector.)