18,533 reputation
334138
bio website math.berkeley.edu/~theojf
location Berkeley
age 28
visits member for 4 years, 6 months
seen yesterday

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.


Apr
14
comment What is Chern-Simons theory expected to assign to a point?
A too-coarse but perhaps useful analogy is with $\sqrt{2}$. The rational number $2$ does not have a rational square root (a fact for which one Pythagorean famously committed suicide by drowning, since this discovery was so heretical). But you can find an analytic context, namely $\mathbb R$, where it does have a square root. The reason this analogy is not too far off is that $Z(C)$ is something like "$C^2$", and in particular $\dim Z(C) = (\dim C)^2$, and $\dim (SL(2)_1) = 2$ (loops-$sl(2)$-reps at level $1$).
Apr
14
comment What is Chern-Simons theory expected to assign to a point?
This is correct, although with the following caveat. The statement "The category of $U_q$-modules you mention is certainly not the center of any other category." depends on what "any other category" may range over. The statement is true if you work with "just categories". Andre's proposal in a different answer involves switching to a more analytical setting, where no longer are hom-sets "just sets" (or "just abelian groups"), but rather topological vector spaces, and where the statement may fail.
Apr
2
comment About Blind Mathematicians
There are some very valuable questions here, which I am interested to hear the answers to but don't know myself. But my feeling is that meta.mathoverflow is the better environment for the second question, and I don't know matheducators.stackexchange but expect it's good for the first. I have voted to move this question to meta.
Mar
30
answered Rank vanishing in tensor categories
Mar
25
comment What is a Homotopy between $L_\infty$-algebra morphisms
@Mark.Neuhaus No, of course not. Things go funny if you're not over a (commutative) ring containing $\mathbb Q$, but that's really the only condition. That said, if $W$ is defined over $R$ and $R \supseteq \mathbb Q$, then $W \otimes_R R[\dots] = W \otimes_{\mathbb Q} \mathbb Q[\dots]$. So there's also no gain.
Mar
13
comment What is geometric engineering in quantum field theory?
A good resource for constructing MO questions is meta.mathoverflow.net/questions/70.
Mar
12
comment Adjoining adjoints in a 2-category
I think I remember Jeffrey Morton telling me something similar --- that for an n-category C, the category of Spans in C (or perhaps spans of spans, k times) is the universal n-category receiving a functor from C in which every morphism is (k-) dualizable. If I have misremembered this, then it is entirely my fault, and not Jeffrey's.
Mar
10
reviewed Leave Open Sources in unimodular rows
Mar
10
reviewed Leave Open The largest size of a boolean subgraph (a hypercube) of a given graph
Mar
5
awarded  Popular Question
Mar
4
comment Which endomorphism algebras are not Morita-trivial?
@მამუკაჯიბლაძე I don't know much about ring spectra, but I'd love to learn. Maybe you can describe some such examples in an answer?
Mar
4
comment Which endomorphism algebras are not Morita-trivial?
@WillSawin Yes, I believe that will work. So the reason I tend to believe (mistakenly) that all endomorphism algebras are Morita trivial is because Vect does not split as a product of categories (so the only non-Morita-trivial endomorphism algebra is 0).
Mar
4
awarded  Popular Question
Mar
3
asked Which endomorphism algebras are not Morita-trivial?
Mar
2
reviewed Close Galois groups and braid groups
Mar
2
reviewed Close Minimal piecewise-linear knot diagram
Feb
21
awarded  Nice Answer
Feb
12
comment Is this knot invariant already treated somewhere in the literature?
Other than by knowing a complete set of diagrams for K, is there any way to compute S(K)?
Feb
8
accepted A geometric characterization of Rees algebras in categories without Choice
Feb
5
answered When does a monoidal functor between ribbon categories preserve cups and caps, but not necessarily braidings?