1,484 reputation
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bio website math.utoronto.ca/jmfisher
location Toronto
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visits member for 3 years, 2 months
seen Aug 18 at 17:34

I'm a PhD candidate interested in mathematics inspired by theoretical physics (QFT, strings, integrable systems, etc.).


Aug
3
revised Asymptotic behavior of a sequence based on a subsequence.
deleted 177 characters in body
Aug
3
comment Asymptotic behavior of a sequence based on a subsequence.
I didn't realize that $m$ is supposed to be fixed. I'll update my answer when I get a chance.
Aug
3
answered Asymptotic behavior of a sequence based on a subsequence.
Jun
24
awarded  Yearling
May
1
comment What is the Lie algebra of the ``indefinite orthogonal group''?
Just to add--these are all non-compact real forms of the corresponding complex groups $O(n, \mathbb{C})$, etc. So from the point of view of their complex representations, the signature $(p,q)$ does not really play a role. But the signature does play a role in the real representation theory (see e.g. the classification of spinors, which exhibits mod 8 periodicity).
Apr
28
answered Approximating the Hessian
Apr
28
awarded  Supporter
Apr
27
answered An isomorphism in relative De Rham cohomology
Apr
27
awarded  Commentator
Apr
27
comment An isomorphism in relative De Rham cohomology
I'm a bit confused. If $E \to M$ is a vector bundle, then $M$ is a retract of $E$ and they have the same cohomology. It seems to me that the relative cohomology $H^\ast(E, E^o)$ should be isomorphic to the (reduced?) cohomology of the Thom space of $E$, which is certainly not isomorphic to $H^\ast(M)$ in general.
Apr
26
answered Scalar product on manifold.
Apr
25
comment Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
@Kally what is your working definition of polynomial differential operators, if not the algebra generated by $x_i, \partial_j$ subject to the above relations? There are several equivalent definitions, so the answer depends on which you take as fundamental.
Apr
25
answered Reference request for “Hodge Theorem”
Apr
15
answered Symplectic positive definite matrix.
Apr
14
answered Numeric methods for ordinary differential equations
Apr
14
comment Embedding/Submersion Properties of Cotangent Maps (Pullbacks)
Yes, $d\phi$ (or $\phi_\ast$, or $T\phi$) is the differential of $\phi$. I think (4) should be true as well, since $\phi$ will be a diffeomorphism on the total spaces and it is linear on the fibers.
Apr
14
answered Embedding/Submersion Properties of Cotangent Maps (Pullbacks)
Apr
13
comment Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
Updated to include a sketch of the proof. You can find the details in the lecture notes by Cannas da Silva.
Apr
13
revised Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
added 1002 characters in body
Apr
13
answered formal glueing of schemes