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bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 23
visits member for 3 years, 8 months
seen 6 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.


Apr
17
answered What's the best strategy to count the eggs in the jar?
Apr
17
comment Topological invariance of chern classes
I don't think so. The Chern classes of a vector bundle are certainly a topological invariant of the vector bundle. The issue here is that we're taking the Chern class of the (complexified) tangent bundle, and a homeomorphism isn't guaranteed to have the property that the pullback of the complexified tangent bundle is the complexified tangent bundle. Indeed up to homeomorphism one cannot even recover the smooth structure in general.
Apr
17
answered Lie algabra of R^n
Apr
17
comment Comparing coefficients in finite field
The correct statement is that $(a + b)^p = a^p + b^p$ for any $a, b$ in a commutative ring of characteristic $p$, e.g. in the polynomial ring $\mathbb{F}_p[x]$. In particular, you can conclude that $(1 + x)^p \equiv 1 + x^p \bmod p$ but not a stronger statement than this.
Apr
17
comment Exact meaning of “Not every matrix is a tensor”.
I can't make any sense of that statement. Every square matrix is a $(1, 1)$-tensor by definition. What's the source?
Apr
15
comment $ax^2 + b$ and infinitely many primes: Does existence proof exist?
This conjecture is open for all polynomials of degree greater than one, as far as I know.
Apr
15
comment What is the definition of a norm in the context of rings?
Different definitions are suitable in different contexts. Some of those contexts are sophisticated. I wouldn't worry too much about it at this point.
Apr
15
comment distance Pure Math graduate programs?
A distance learning graduate program doesn't seem like a good idea. Probably most of the value of being in a graduate program comes from being immersed in a physical environment with your fellow grad students and professors.
Apr
15
answered What is the reason for stating Cayley's theorem this way?
Apr
15
comment Why is $\mathsf{HTAG}$ (Hausdorff, Topological, Abelian Groups) preabelian?
Which axiom are you having trouble verifying?
Apr
14
comment How to motivate the axioms for the inner product
@P-i-: en.wikipedia.org/wiki/Polarization_identity
Apr
14
comment Surjectivity and exactness on higher homotopy groups
en.wikipedia.org/wiki/…
Apr
13
answered Intuitive significance of harmonicity
Apr
12
comment What is the categorical diagram for the tensor product?
@user: that was not at all clear from your other two comments. Yes, one general case is when the monoidal category is closed.
Apr
12
awarded  Nice Answer
Apr
11
comment What is the categorical diagram for the tensor product?
@user: the tensor product is an example of a monoidal operation. Are you asking how to verify, from the universal property, that it satisfies the axioms? To do this, write down a universal property that is satisfied by the $n$-fold tensor product.
Apr
11
comment If the functor on presheaf categories given by precomposition by F is ff, is F full? faithful?
I'm a little confused about the last part of the question; I'm not sure exactly how it's supposed to be added to the other conditions.
Apr
11
comment What is the categorical diagram for the tensor product?
@user: I still don't understand the question.
Apr
10
comment Can a ring isomorphism change the structure of a module?
The similarity is that any ring automorphism of $R$ induces an automorphism of the category of $R$-modules, and automorphisms of categories preserve categorical properties (like the structure of the lattice of subobjects, etc.).
Apr
10
comment Why does the tensor product of an irreducible representation with the sign representation yield another irreducible representation?
@Eric: $L^{\ast}$ is the dual representation (en.wikipedia.org/wiki/Dual_representation). That's the correct description for one-dimensional representations, but in general you also need to take the transpose (thinking of the target as being matrices).