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location New Jersey
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visits member for 4 years
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Graduate student in mathematics.


Feb
1
comment Why is the Laplacian important in Riemannian geometry?
Here's something you may appreciate: associated to a differentiable operator is its symbol, which is a tensor that encodes the highest order part of the operator. The symbol of the Laplacian is the metric tensor.
Feb
1
comment How are continuity of real and imaginary part related to continuity of the function?
ok looks good now :-)
Feb
1
comment How are continuity of real and imaginary part related to continuity of the function?
yea good point.
Feb
1
answered How are continuity of real and imaginary part related to continuity of the function?
Feb
1
revised How are continuity of real and imaginary part related to continuity of the function?
edited tags
Feb
1
reviewed Approve suggested edit on Integral of square root of a fraction of two functions
Jan
30
comment Pullback of a form using the Hopf fibration
Since $S^3 \to S^2$ is a principal $S^1$ bundle, the map $H^* : \Omega^\bullet(S^2)\to \Omega^\bullet(S^3)$ gives an iso between $\Omega^\bullet(S^2)$ and the basic forms on $S^3$ (those forms $\mu$ which satisfy $i_v \mu = 0$ for all $v \in \ker H_*$ and $R_z^* \mu = \mu$ for all $z \in S^1$). $S^2$ is oriented and two-dimensional, so there is a unique basic 2-form on $S^3$ up to multiplication by functions pulled back from a function on $S^2$. So if you can show that $\omega$ is basic then you get $H^* (f \alpha) = \omega$ for some $f \in C^\infty(S^2)$. Not sure how to show f is const.
Jan
19
comment Commuting matrices and simultaneous diagonalizability
@DustanLevenstein you're right. For some reason I was thinking that $G$ was an abelian group generated by those matrices, not necessarily equal to it.
Jan
19
comment Commuting matrices and simultaneous diagonalizability
As stated the result is false. you need to assume that for each $M_i$ there is some $T_i$ such that $T_i M_i T_i^{-1}$ is diagonal. Then the question should be to show that one can choose $T_i$ to be the same across $i$.
Jan
19
comment Commuting matrices and simultaneous diagonalizability
I'm guessing you want to assume that each $M_i$ itself is diagonalizable?
Jan
8
reviewed Approve suggested edit on resolving integral using gamma function
Jan
8
revised Hilbert's syzygy theorem in the analytic setting
added 2 characters in body
Jan
8
comment Hilbert's syzygy theorem in the analytic setting
@Marek you're right, thanks for the correction. I have edited it accordingly.
Jan
8
revised Hilbert's syzygy theorem in the analytic setting
added 7 characters in body
Jan
8
asked Hilbert's syzygy theorem in the analytic setting
Dec
29
reviewed Approve suggested edit on Order of a cyclic group with a single proper subgroup of order 7
Dec
29
reviewed Approve suggested edit on find general solution to the Differential equation
Dec
29
reviewed Approve suggested edit on find general solution to the Differential equation
Dec
20
comment Resolution of direct image functor
I think this only holds for smooth submanifolds of $\mathbb CP^n$
Dec
20
asked Resolution of direct image functor