20,138 reputation
447155
bio website math.berkeley.edu/~theojf
location Berkeley
age 29
visits member for 5 years, 3 months
seen 3 hours ago

I am a recent graduate from UC Berkeley. Starting Fall 2013, I am a Boas Assistant Professor at Northwestern University. My research is broadly centered on quantum field theory — my interests include category theory, representation theory, homological algebra, algebraic topology, Poisson geometry, and theoretical physics.


2d
comment Can ZFC prove it cannot derive an inconsistency in $n$ steps?
Fascinating! (I saw this as a non-logician, although I teach a freshman "writing" seminar on logic.)
Jan
24
awarded  Revival
Jan
21
comment PBW for Lie Superalgebras
So the theorem in fact states that a basis for $U\mathfrak{sl}(2|1)$ consists of the monomials $H_1^aH_2^bE_1^cF_1^dE_2^eF_2^f[E_1,E_2]^g[F_1,F_2]^h$, or some such, with $e,f,g,h \in \{0,1\}$.
Jan
21
comment PBW for Lie Superalgebras
I think you have misinterpreted the statement of PBW. Indeed, $E_\theta = [E_1,E_2]$ and $F_\theta = [F_1,F_2]$ are homogeneous basis elements of $\mathfrak{sl}(2|1)$, and hence allowed monomial generators in the PBW theorem. Compare $\mathfrak{sl}(3)$, which is generated by $H_i,E_i,F_i$ for $i=1,2$, but which again includes two extra basis elements.
Jan
8
comment Reference for “multi-monoidal categories”
Almost surely what you've written down is an action of the operad Assoc on a category. The equivalence with the standard definition is probably "implicit in results of Mac Lane", or some such muttering. I'm reminded of a definition of "symmetric monoidal category" that I think I saw in a paper of Deligne's (although I don't remember where exactly) that asks for a functor $\mathcal C^S \to \mathcal C$ for each finite set $S$, with natural maps that include the permutations of $S$. So if you think the coherences are correct (I didn't check carefully), then go ahead and use it!
Jan
6
awarded  Popular Question
Jan
5
awarded  Nice Answer
Jan
5
awarded  Good Question
Jan
3
comment Integrating Poisson groups
Good, that's farther than I had managed last night. (And it looks like, as I requested, my badly-formatted comment was deleted.) Infinitesimally, $\mathrm{pt} \to \mathrm B G$ is not just coisotropic, but sub-Poisson, so I expect that to remain true at the level of simplicial manifolds as well. Note that the double, being endowed with a metric, receives a 2-shifted symplectic structure on its classifying space; this should be analogous to the symplectic structure on the morphisms in the symplectic groupoid.
Jan
3
revised Singularity-free isotopies between string diagrams for monoidal categories
Extended the answer
Jan
3
reviewed Close Is there a pairing function from countable ordinals to $\mathbb N$?
Jan
3
reviewed Close homotopy groups of spheres.
Jan
3
reviewed Close equivalence in simplicial category
Jan
3
reviewed Leave Open Gaussian distributions as fixed points in Some distribution space
Jan
3
comment Singularity-free isotopies between string diagrams for monoidal categories
@JamieVicary Ah, good, so I did not understand your question correctly. I guess I was assuming that if your object was 1-dualizable (I mean, has both duals, which each have both duals, etc.) then you were allowing that data in the diagram. In any case, I'm sure you have favorite examples where this happens for every object, but generally left and right duals are not isomorphic at all.
Jan
2
answered Singularity-free isotopies between string diagrams for monoidal categories
Jan
2
awarded  Good Question
Dec
21
comment Cantor's theorem for presheaves?
@AndrejBauer I'm not sure what Lawvere's fixed-point theorem is, but isn't the conclusion of Cantor's theorem the statement that Set has a fixed-point free map, namely the power set functor?
Dec
18
comment Lurie's approach to the bar-cobar adjunction
I think in "where $\mathcal C$ is the $\infty$-category of Kan complexes" you mean $\mathcal C$ to be $\mathcal S$.
Dec
15
comment Does the $(\mathbb Z/2)$-graded isomorphism $E_n \cong E_{n+2}$ have any nice properties?
@DavidTreumann Good question! Here's my understanding. There is a semidirect product $O(n) \ltimes E_n$ called "framed $E_n$", and its formality makes it isomorphic to what you get by adjoining to $P_n$ a generator that acts as primitive of the bracket in the Hochschild cohomology coming from the commutative multiplication. The isomorphism $P_n \cong P_{n+2}$ is compatible with this extra generator. So I think that there is a sense in which the isomorphism $E_n \cong E_{n+2}$ is equivariant for some sort of $O$ action, but I'd have to think a while to unpack the details.