51,942 reputation
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bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 24
visits member for 5 years, 9 months
seen 57 mins ago

I am a third-year graduate student at UC Berkeley. I'm interested in the interplay between homotopy theory, quantum field theory, manifold topology, and higher category theory.


8h
comment SO$(4)$ (& SO$(n)$) characterization?
Added line breaks where your paragraphs were. Hope you don't mind.
8h
revised SO$(4)$ (& SO$(n)$) characterization?
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13h
comment Virasoro-like algebras over the quaternions
@Chanler: if you just write down the standard definition as applied to a left $\mathbb{H}$-module, you get a definition which doesn't apply to $\mathfrak{gl}_n(\mathbb{H})$ (the Lie bracket on $\mathfrak{gl}_n(\mathbb{H})$ fails to be $\mathbb{H}$-bilinear in the appropriate way). Are you sure that's what you want?
22h
comment Virasoro-like algebras over the quaternions
What is a Lie algebra over $\mathbb{H}$? (The Lie operad is a symmetric operad in, say, abelian groups, so I know how to define a Lie algebra in any symmetric monoidal $\text{Ab}$-enriched category. But $\mathbb{H}$-modules aren't such a category.)
22h
answered SO$(4)$ (& SO$(n)$) characterization?
1d
comment Why only Normed Linear Spaces?
We do in fact do this. See, for example, en.wikipedia.org/wiki/Absolute_value_(algebra) and en.wikipedia.org/wiki/Banach_algebra.
2d
revised Does the following characterize local presentability?
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2d
answered Does the following characterize local presentability?
Jul
28
comment Does every Lawvere theory arise in this way?
@David: no, that already fails in the case of groups. The way you recover a Lawvere theory from the free algebra over it on one generator $X$ is by taking the opposite of the full subcategory on the finite coproducts of $X$, not by taking the full subcategory on the finite products of $X$.
Jul
26
comment Is there a generalization of homotopy groups to fractional dimensions
Is there an $E_{\infty}$ ring spectrum $E$ and an invertible $E$-module spectrum $F$ such that $F^{\otimes 2} \cong E[1]$? ($\otimes$ here denotes the $E$-module smash product.) This gives a notion of fractional $E$-homology and cohomology.
Jul
24
comment Loop space generalization
$S^1$ has two interesting kinds of extra structure as an object of the homotopy category of based spaces: first, it's a cogroup object, but second, it's a group object. The first kind of extra structure is the one related to loop spaces, while the second kind of extra structure is the one related to its description as $B \mathbb{Z}$. The Eilenberg-MacLane spaces $B^n \mathbb{Z}, n \ge 2$, on the other hand, are only group objects, and have no cogroup structure (since their cohomology has interesting cup products).
Jul
22
awarded  Good Question
Jul
22
awarded  Good Question
Jul
22
awarded  Nice Question
Jul
21
comment Three questions about modular forms frequently asked to me
Crossposted: math.stackexchange.com/questions/1369276/…
Jul
21
answered When is the adjoint to a monoidal functor monoidal?
Jul
17
awarded  Notable Question
Jul
17
awarded  Notable Question
Jul
16
comment homotopy equivalence between configuration spaces on non-homeomorphic spaces
The general statement is that the configuration space of $k$ points on a manifold $M$ with boundary is homotopy equivalent to the configuration space of $k$ points on $\text{int}(M)$.
Jul
15
awarded  Enlightened