19,530 reputation
442151
bio website math.berkeley.edu/~theojf
location Berkeley
age 29
visits member for 5 years
seen 8 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.


8h
accepted Which real Pin groups agree?
1d
comment Chiral categories versus braided monoidal categories
I think it's not quite right to think of a chiral algebra as an $E_2$ algebra. The latter should give examples of the former (up to some framing, perhaps), but chiral algebras should not, in general, be "locally constant". Think about a much less categorical setting of functions. Locally constant functions are very different from holomorphic functions. Or am I misunderstanding the notion of "chiral algebra" --- is there a "de Rham" that I missed somewhere?
Oct
29
comment What are the “correct” conventions for defining Clifford algebras?
I second @KConrad, since you can walk down the hall and knock on his door --- my memory is that he is often in, and usually happy to talk to graduate students. And he certainly is sensitive to other conventions issues related to Clifford algebras in his Lie theory classes. If you get an answer, do be sure to post it here, of course.
Oct
24
comment Which real Pin groups agree?
Great, I'll take a look.
Oct
24
awarded  Nice Question
Oct
24
comment Which real Pin groups agree?
Why does $\phi$ commute with $\tau$? Indeed, let $\phi: \mathrm{Cliff}(4,0) \to \mathrm{Cliff}(0,4)$ be the isomorphism. It identifies a generator $x$ with a cubic $yzw$ (for some arbitrary ortho(normal up to sign) bases). Then $\phi(\tau(x)) = \phi(x) = yzw$, whereas $\tau(\phi(x)) = \tau(yzw) = wzy = -yzw$.
Oct
21
asked Which real Pin groups agree?
Oct
19
comment “Nice” functions on infinite-dimensional space of germs of continuous functions at a point
... with respect to analytic functions is $\mathrm{Spec}($this subring$)$.
Oct
19
comment “Nice” functions on infinite-dimensional space of germs of continuous functions at a point
I agree that $\mathrm{Spec}(\mathbb C\llbracket(a-x)\rrbracket)$ is an (I hesitate to say "the") infinitesimal neighborhood the point $x=a$. But it is not the neighborhood on which germs of analytic functions are defined, which is a little bigger. Indeed, an analytic function has a power series whose radius of convergence is positive; this happens iff the coefficients of the power series grow slower than some exponential. So I would say that $\mathbb C\llbracket(a-x)\rrbracket$ has a subalgebra consisting of those power series with positive radius of convergence, and the germ of a point ...
Oct
16
awarded  Favorite Question
Oct
11
awarded  Enlightened
Oct
11
awarded  Nice Answer
Oct
9
asked What suffices to check completeness in an n-fold Segal space?
Oct
7
awarded  Enlightened
Oct
7
awarded  Nice Answer
Oct
6
awarded  Yearling
Oct
2
comment Homotopy Transfer Theorem for Differential Graded Associative Algebras
Hrm, they were on my old site. I'll try to find them.
Sep
30
awarded  Explainer
Sep
21
awarded  Nice Question
Sep
20
comment Learning roadmap in Algebra
Great question, but I think math.stackexchange would be a better host for it.