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bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 24
visits member for 5 years, 1 month
seen 7 mins ago

I am a third-year graduate student at UC Berkeley. I'm interested in the interplay between homotopy theory, quantum field theory, manifold topology, and higher category theory.


8h
comment 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
comment 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
comment If 2-manifolds 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
comment If 2-manifolds 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 3-manifolds see en.wikipedia.org/wiki/Moise%27s_theorem.
2d
awarded  Popular Question
2d
comment Partitions with each part dividing the original number
OEIS entry: oeis.org/A018818
2d
comment 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
comment When does $\mathbf{Top}/X$ embedd fully faithfully into $\mathbf{Top}$?
But... why would you want such a thing?
Nov
21
comment 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
comment Why do Bernoulli numbers arise everywhere?
I don't see how any of this explains why Bernoulli numbers show up in topology.
Nov
18
comment amenable + without $BS(m,n)$+finite $K(G,1)$implies virtually cyclic?
Anyway, this seems like it would be better on MO.
Nov
18
comment 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
comment Can one classify irreducible unitary representations of the Weyl algebra?
en.wikipedia.org/wiki/Stone%E2%80%93von_Neumann_theorem
Nov
17
comment 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.