bio  website  math.berkeley.edu/~qchu 

location  Berkeley, CA  
age  24  
visits  member for  5 years, 8 months 
seen  3 hours ago  
stats  profile views  61,951 
I am a thirdyear graduate student at UC Berkeley. I'm interested in the interplay between homotopy theory, quantum field theory, manifold topology, and higher category theory.
5h

comment 
free action on product of two spaces
This is not even true if $G, X, Y$ are all finite. 
5h

awarded  Enlightened 
10h

comment 
What is the reverse mathematical strength of the fundamental theorem of algebra?
Does Harvey Friedman's claim refer to the consistency of firstorder PA or of secondorder PA? 
Jun 26 
comment 
Existence of nontrivial characters on compact abelian group
Fair enough; maybe I should have said "this is an aspect of Pontryagin duality." The most important thing, I think, was to communicate that there was a common keyword the OP could use to find out more. 
Jun 26 
awarded  Good Question 
Jun 26 
comment 
Existence of nontrivial characters on compact abelian group
en.wikipedia.org/wiki/Pontryagin_duality#References 
Jun 26 
comment 
Existence of nontrivial characters on compact abelian group
Yes; in fact you can relax "compact" to "locally compact." This follows from Pontryagin duality. 
Jun 23 
comment 
Do representations of the universal enveloping algebra $\mathrm{U}\mathfrak{su}_2$ retain the Hopf algebra structure?
Oh, I misread your question. I think your truncation is not a Hopf algebra. 
Jun 23 
comment 
Do representations of the universal enveloping algebra $\mathrm{U}\mathfrak{su}_2$ retain the Hopf algebra structure?
If two algebras are isomorphic and one of them has an additional Hopf algebra structure then you can transport that structure along the isomorphism; this is called, as you might expect, "transport of structure." 
Jun 18 
revised 
Higher refinement of Seifertvan Kampen theorem on the language of hocolim
deleted 14 characters in body 
Jun 18 
answered  Higher refinement of Seifertvan Kampen theorem on the language of hocolim 
Jun 16 
comment 
Categorical definition of infinite symmetric product
I don't see any reason to expect a monomorphism. The natural map $S_n \to \text{Aut}(X^{\otimes n})$ is often not a monomorphism, for example. 
Jun 16 
comment 
$\Omega X$action on spectral $X$bundles
@Jon: the data of an action of a grouplike $E_1$ space $G$ on an object of an $\infty$category $C$ is precisely the data of a functor $BG \to C$. So the data of a functor $X \to C$ is precisely the data of a functor $B \Omega X \to C$, which is in turn precisely the data of an $\Omega X$action on an object of $C$. 
Jun 15 
awarded  Nice Answer 
Jun 14 
comment 
$\Omega X$action on spectral $X$bundles
$X$ needs to be a based and connected space. 
Jun 14 
comment 
What are algebras for the little nballs/ncubes/nsomething operads exactly?
$E_1$ algebras in a symmetric monoidal (higher) category themselves form a symmetric monoidal (higher) category, and one way to define an $E_2$ algebra is that it is an $E_1$ algebra in $E_1$ algebras. This generalizes: an $E_n$ algebra is an $E_k$ algebra in $E_{nk}$ algebras. So by induction, you're just repeatedly passing to the $E_1$ algebras in what you had before. 
Jun 14 
comment 
What are algebras for the little nballs/ncubes/nsomething operads exactly?
@Mark: it just means I can't describe them at a fixed category level, like I did for $n = 2$ where I could just use groupoids. For example, you might've expected that I can describe the $E_3$ operad as an operad in $2$groupoids or something, but that's not true. And of course the compatibility can be made precise in general: it's made precise by the $E_n$ operads! This may seem not very explicit but that's the price to pay for doing the homotopically correct thing. I don't really know what you mean by "algorithm" here but here is one way to think about it: (cont) 
Jun 14 
comment 
Why there is a relation among the secondorder minors of a symmetric $4\times 4$ matrix?
@Robert: thanks! (I was confused about how to interpret the minors of a symmetric matrix interpreted as a quadratic form; I know how to do it for linear maps, which is why I was confused about whether I needed an inner product.) 
Jun 14 
comment 
Why there is a relation among the secondorder minors of a symmetric $4\times 4$ matrix?
Can you elaborate on why these are the right plethysms to look at? I'm afraid I don't quite see it. (In particular I'm confused about whether or not I need to introduce an inner product on $V$ to make sense of the question.) 
Jun 13 
comment 
Z/p action on finite contractible complex
I also don't know what argument you have in mind for the manifold case. Say $p = 2$. Why can't there be three fixed points with indices $1, 1, 1$? 