147,140 reputation
14307559
bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 23
visits member for 3 years, 11 months
seen 1 hour ago

I'm a second-year graduate student in pure mathematics at UC Berkeley. You can contact me at qchu[at]math[dot]berkeley[dot]edu.


1h
comment Why are Lie Groups so “rigid”?
Of course it is possible to turn an ellipse into a Lie group, since ellipses are diffeomorphic to circles.
13h
comment Stiefel-Whitney classes of 3-manifolds are trivial
@Peter: ah, that explains things. In any case there are several ways to see that $S^1 \times \mathbb{RP}^2$ is not orientable. More generally, $M \times N$ is orientable iff $M$ and $N$ are orientable. One can also compute using the Kunneth formula that $H^3(S^1 \times \mathbb{RP}^2, \mathbb{Q})$ vanishes.
13h
comment Stiefel-Whitney classes of 3-manifolds are trivial
@Peter: it is not implied by that fact. $w_1$ being nonzero doesn't imply that the Stiefel-Whitney numbers are nonzero. My copy of Milnor-Stasheff only says "$3$-manifold"; it doesn't even say "closed," so I wouldn't be surprised if there was a standing assumption about orientability that wasn't made explicit or something like that.
13h
answered Stiefel-Whitney classes of 3-manifolds are trivial
14h
comment When does $n$-dimensional algebra have $m$-dimensional faithful representation?
It depends on what you mean by "know." I wouldn't be surprised if this problem were undecidable for arbitrary finite-dimensional algebras.
1d
comment How much math is there?
@Joel: I seriously doubt that affects the order of magnitude of the answer, and it's probably not useful to try to pin down the answer to this question, whatever it could mean, more precisely than that.
1d
comment How much math is there?
A start: MathSciNet has a total of 3 million publications (ams.org/mathscinet).
2d
answered Is an arbitrary group generated by a traversal of the conjugacy classes?
2d
comment Basic Notions of Categorification
homology is of course more than a function on objects; it's also a functor.
2d
comment Basic Notions of Categorification
A categorification of a map between sets should be a functor between categories. Categorification is a big topic so it really depends on what you're interested in.
2d
comment Rational analysis
@Gaussler: I don't know what you mean by "the inverse of a rational function is rational." By "rational function" do you mean a function $\mathbb{R} \to \mathbb{R}$ which sends $\mathbb{Q}$ to $\mathbb{Q}$? If so, this is clearly false; for example, $x \mapsto x^3$ is rational but its inverse isn't.
2d
comment Rational analysis
You can't prove anything interesting without the intermediate value theorem.
Jul
21
comment Why are compact and noncompact manifolds without boundary called closed manifolds and open manifolds, respectively?
Historical inertia.
Jul
20
comment Finding a lie group structure on $\mathbb R^n\setminus\{0\}$
@jspecter: you mean a compact connected Lie group of positive dimension. This is false if any of those hypotheses are dropped: $\mathbb{R}$ has Euler characteristic $1$, $\mathbb{Z}_2$ has Euler characteristic $2$, there are topological groups without a well-defined Euler characteristic...
Jul
20
comment What is the importance of $\pi$ in mathematics?
$\pi$ is extremely important but it's extremely unimportant to determine its digits.
Jul
20
comment Should I read about Manifolds or Algebraic Topology?
@user: reading one math book instead of two does not in any reasonable sense constitute focusing your energy. The division of mathematics into subjects, and of facts about mathematics into books, is mostly an illusion, especially in this case. Learning about manifolds will enrich your understanding of algebraic topology and vice versa.
Jul
20
comment Finding a lie group structure on $\mathbb R^n\setminus\{0\}$
$\mathbb{R}^n \setminus \{ 0 \}$ can't have a Lie group structure for $n$ odd and greater than $1$ because it's homotopy equivalent to $S^{n-1}$ and in particular has Euler characteristic $2$. But a connected Lie group of positive dimension has Euler characteristic either $0$ or $1$.
Jul
20
comment Can any of the exotic differentiable structures on $\mathbb R^4$ make $GL(\mathbb R^2)$ into an 'exotic' Lie group structure?
The $\mathbb{R}^4$ cannot be exotic because the isomorphism to a standard $\mathbb{R}^4$ is linear, and in particular smooth. $\text{GL}_2(\mathbb{R})$ is not even homotopy equivalent to $\mathbb{R}^4$.
Jul
20
comment Is every local ring the localization of some other ring?
I was assuming the OP would add more conditions (e.g. connected).
Jul
20
comment What does it mean to demonstrate “por doble inclusión” in Spanish?
"Inclusion" and "union" shouldn't take as input two sets; they should take as input two subsets of a set. For example, the question of whether $\mathbb{Q}[x]/(x^3 - 2)$ is a subset of $\mathbb{Q}[x]/(x^3 - 3)$, or of what their union is, is meaningless; you need to pick an embedding of these two fields into, say, $\mathbb{C}$ to make this question meaningful, and the answer depends on the choice of such an embedding.