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grad student at upenn.

Mar
30
comment Atiyah classes of holomorphic vector bundles with trivial Chern classes
@PavelSafronov Err, now I'm confused. Topologically we have $\mathcal (O(-1)\otimes \mathcal O(-1))\oplus \mathbb C = \mathcal O(-1) \oplus \mathcal O(-1)$. So topologically, $\mathcal O(1) \oplus \mathcal O(-1) = \mathbb C^2$ is trivial and so admits a flat connection.
Mar
30
comment Atiyah classes of holomorphic vector bundles with trivial Chern classes
@PavelSafronov Thanks. Also I just realized since $\pi_1(\mathbb P^1) = 0$ the only flat rank 2 vector bundle is trivial.
Mar
30
accepted Atiyah classes of holomorphic vector bundles with trivial Chern classes
Mar
30
comment Atiyah classes of holomorphic vector bundles with trivial Chern classes
Thanks for the answer! Do you happen to have a reference for the theorem of Weil? Also, do you know offhand if $\mathcal{O}_{\mathbb{P}^1}(p)\oplus \mathcal{O}_{\mathbb{P}^1}(-p)$ admits a flat connection?
Mar
30
revised Atiyah classes of holomorphic vector bundles with trivial Chern classes
edited title
Mar
30
asked Atiyah classes of holomorphic vector bundles with trivial Chern classes
Mar
26
comment Geometric Quantization
@SanathDevalapurkar Sorry, what I meant is that for a general configuration space there is no known canonical way to quantize it. The point is that geometric quantization gives one method to quantize a space that satisfies certain conditions. That this is a "correct" approach comes down to it satisfying certain axioms a quantization should have and agreeing in the simple cases with what physicists expect (e.g. on $\mathbb R^n$ or $S^2$).
Mar
26
comment Geometric Quantization
@SanathDevalapurkar this is no general method of quantization. I would check out these mathoverflow posts mathoverflow.net/questions/6200/what-is-quantization mathoverflow.net/questions/8606/…
Mar
26
comment Geometric Quantization
@SanathDevalapurkar are you able to see why if you start with $X = \mathbb R^n$ you get the usual quantization of first year quantum courses?
Mar
14
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Jan
21
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Jan
13
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Jan
12
comment Hilbert's syzygy theorem in the analytic setting
@user76758 thanks. maybe you should make your comment an answer. also, do you have good references for these statements? thanks.
Jan
9
asked Hilbert's syzygy theorem in the analytic setting
Aug
26
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Aug
26
revised lie-groups wiki excerpt
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Aug
26
suggested suggested edit on lie-groups tag wiki excerpt
Jul
24
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Jun
14
accepted Are all representations of $G\times H$ induced from representations of $G$ and $H$?
Jun
11
comment Are all representations of $G\times H$ induced from representations of $G$ and $H$?
Thanks for the nice counterexample!