147,010 reputation
14307559
bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 23
visits member for 3 years, 11 months
seen 7 hours 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.


10h
answered Is an arbitrary group generated by a traversal of the conjugacy classes?
17h
comment Basic Notions of Categorification
homology is of course more than a function on objects; it's also a functor.
18h
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.
19h
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.
22h
comment Rational analysis
You can't prove anything interesting without the intermediate value theorem.
1d
comment Why are compact and noncompact manifolds without boundary called closed manifolds and open manifolds, respectively?
Historical inertia.
1d
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...
1d
comment What is the importance of $\pi$ in mathematics?
$\pi$ is extremely important but it's extremely unimportant to determine its digits.
1d
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.
1d
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 $1$.
1d
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 $\mathbb{R}^4$.
1d
comment Is every local ring the localization of some other ring?
I was assuming the OP would add more conditions (e.g. connected).
1d
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.
1d
comment Should I read about Manifolds or Algebraic Topology?
Both. Just read both.
2d
comment Constructing an indicator function from a braid group which represents 'all strings have returned to their initial position'.
Take the natural map $B_n \to S_n$. What you want to know is just whether the image is the identity or not. (The sign homomorphism doesn't tell you this.) The bit of information you're asking for isn't a homomorphism but in some sense this natural map $B_n \to S_n$ ought to be the closest approximation of it by a homomorphism so I think you should just use that instead.
2d
accepted What structure does the alternating group preserve?
2d
accepted What's the point of studying topological (as opposed to smooth, PL, or PDiff) manifolds?
2d
comment What does it mean to demonstrate “por doble inclusión” in Spanish?
:( ${}{}{}{}{}$
2d
comment Fibonacci number that ends with 2014 zeros?
@Yann: the Fibonacci recurrence is reversible, so showing that the Fibonacci sequence is eventually periodic shows that it's always periodic.
2d
comment Is every local ring the localization of some other ring?
Sure; if $R$ is a local ring, then it's a localization of $R \times k$ for any other commutative ring $k$...