19,468 reputation
442150
bio website math.berkeley.edu/~theojf
location Berkeley
age 29
visits member for 5 years
seen 5 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 “Nice” functions on infinite-dimensional space of germs of continuous functions at a point
... with respect to analytic functions is $\mathrm{Spec}($this subring$)$.
2d
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.
Sep
16
awarded  Enlightened
Sep
16
awarded  Nice Answer
Sep
6
comment Recognize this strange expression from linear algebra?
No offense taken. Sorry about misstating the end.
Sep
4
comment When is Rep(U_q(g)) invariant under q -> -q and why?
I don't know if the conventions match yours, but Temperley–Lieb with the circle valued at $\delta = -q^2 - q^{-2}$ is invariant us a monoidal category under $q \mapsto -q$ (of course, since the monoidal category only depends on $q$ via $\delta$), and even as a braided category (via the natural isomorphism that acts by $-1$ on the defining object), but not as a pivotal category.
Sep
4
revised Recognize this strange expression from linear algebra?
admitted an error.
Sep
4
revised Recognize this strange expression from linear algebra?
corrected a 0 to a 2
Sep
3
awarded  Enlightened