bio  website  math.berkeley.edu/~qchu 

location  Berkeley, CA  
age  24  
visits  member for  5 years, 1 month 
seen  7 mins ago  
stats  profile views  54,779 
I am a thirdyear graduate student at UC Berkeley. I'm interested in the interplay between homotopy theory, quantum field theory, manifold topology, and higher category theory.
8h

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It is possible to prove that there is an immersion of the $K3$ surface in $R^8$ using the Mayer integrality theorem?
As far as I can tell this theorem can only give a lower bound on the lowest dimension of an immersion, and it doesn't guarantee that the lower bound is attainable. So there's no way it can guarantee the existence of an immersion. It can only fail to rule it out. 
9h

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It is possible to prove that there is an immersion of the $K3$ surface in $R^8$ using the Mayer integrality theorem?
Maybe I am missing something. Doesn't it in fact follow from the Whitney immersion theorem that K3 immerses into $\mathbb{R}^7$? 
9h

awarded  Enlightened 
10h

awarded  Nice Answer 
22h

awarded  Popular Question 
1d

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If 2manifolds are homeomorphic and smooth, are they diffeomorphic?
Michael, if you'd like to learn more the keywords to look up are "smoothing theory" and "surgery theory." It would probably be easier to ask a new question (after doing some research using these keywords if you still have questions) than to try to get this one reopened. 
2d

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If 2manifolds are homeomorphic and smooth, are they diffeomorphic?
It's a classical result that in dimensions $\le 3$ the smooth, PL, and topological classifications of manifolds coincide; for the case of surfaces see, for example, math.cornell.edu/~hatcher/Papers/TorusTrick.pdf and for the case of 3manifolds see en.wikipedia.org/wiki/Moise%27s_theorem. 
2d

awarded  Popular Question 
2d

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Partitions with each part dividing the original number
OEIS entry: oeis.org/A018818 
2d

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Partitions with each part dividing the original number
Asymptotic estimates will of course depend delicately on the prime factorization of $n$. Would you be happy with a result averaged over many large values of $n$ or are you interested in particular large values of $n$? 
Nov 21 
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When does $\mathbf{Top}/X$ embedd fully faithfully into $\mathbf{Top}$?
But... why would you want such a thing? 
Nov 21 
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When does $\mathbf{Top}/X$ embedd fully faithfully into $\mathbf{Top}$?
That seems like an unnatural thing to ask for in the absence of a natural choice of such an embedding. Why do you want to know? 
Nov 19 
awarded  Enlightened 
Nov 19 
awarded  Nice Answer 
Nov 19 
answered  Robotics, Cryptography, and Genetics applications of Grothendieck's work? 
Nov 18 
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Why do Bernoulli numbers arise everywhere?
I don't see how any of this explains why Bernoulli numbers show up in topology. 
Nov 18 
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amenable + without $BS(m,n)$+finite $K(G,1)$implies virtually cyclic?
Anyway, this seems like it would be better on MO. 
Nov 18 
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amenable + without $BS(m,n)$+finite $K(G,1)$implies virtually cyclic?
What do you mean by a finite $K(G, 1)$? You mean that $K(G, 1)$ can be modeled by a finite CW complex? 
Nov 17 
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Can one classify irreducible unitary representations of the Weyl algebra?
en.wikipedia.org/wiki/Stone%E2%80%93von_Neumann_theorem 
Nov 17 
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Computing $\text{Tor}_*^{R_G} (\mathbb{Z}, \mathbb{Z}) $ for a compact Lie group $G$
In any case, if $G$ is in addition assumed to be connected then $R_G$ is very close to a polynomial algebra and so you should be able to use some kind of Koszul resolution. 