48,171 reputation
14181433
bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 24
visits member for 5 years, 5 months
seen 1 hour 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.


7h
comment Proof that no differentiable space-filling curve exists
@Yemon: oog, yeah, I guess, but in that case I've got nothing intelligent to say.
8h
comment Proof that no differentiable space-filling curve exists
en.wikipedia.org/wiki/Sard%27s_theorem
12h
comment Is there a higher, “orientalish” version of geometric realisation?
I don't understand the question. What do you want this construction to output? An $\infty$-category?
12h
revised Has any attempt been made to classify finite groupoids?
deleted 50 characters in body
12h
comment Has any attempt been made to classify finite groupoids?
@David: hmm, you're right. My bad.
13h
awarded  Necromancer
1d
comment Simply connected Lie groups homeomorphic to R^n are solvable
The reason you need $V$ in this argument is to guarantee that $\mathfrak{k}$ integrates to something compact; the argument fails for $G = \widetilde{SL}_2(\mathbb{R})$ precisely because $\mathfrak{k}$ does not integrate to a compact subgroup of $G$ in that case. You'd like to argue starting from the fact that the Killing form on $\mathfrak{g}_{ss}$ is negative definite on $\mathfrak{k}$, but it doesn't follow that the Killing form on $\mathfrak{k}$ itself is negative definite.
1d
comment Classifying spaces of topological groups whose underlying spaces are homotopy equivalent
$BG$ is fundamentally an object which only makes sense up to weak homotopy equivalence; asking questions like this means getting bogged down in the technicalities of spaces not having the homotopy type of a CW complex and there's just no reason to torture yourself like that.
2d
answered Simply connected Lie groups homeomorphic to R^n are solvable
Mar
27
answered Has any attempt been made to classify finite groupoids?
Mar
26
comment When does the Borel construction have the homotopy type of a CW-complex?
Presumably this depends on a choice of $EG$. What $EG$ are you choosing?
Mar
26
awarded  Nice Answer
Mar
26
awarded  Necromancer
Mar
26
revised UFD and fundamental group
deleted 13 characters in body
Mar
26
comment Stiefel-Whitney class of complex projective spaces
Crossposted: math.stackexchange.com/questions/1206867/…
Mar
26
answered UFD and fundamental group
Mar
25
comment Moduli space of flat connections over a torus
It is not a manifold in general. Lots of stuff is known about these sorts of spaces; one keyword you can use is "character variety."
Mar
25
revised Generators of invariant polynomials of semisimple Lie algebra
added 287 characters in body
Mar
25
comment Moduli space of flat connections over a torus
What do you mean by "known"? The moduli space of flat $G$-connections on a torus is the space $\{ (g, h) \in G^2 : gh = hg \}$ of commuting pairs of elements of $G$ ($g, h$ are given by monodromy around a pair of generators of $\pi_1$) modulo the action of $G$ given by simultaneous conjugation. What does it mean to know this space?
Mar
25
answered What is an infinite prime in algebraic topology?