bio  website  math.rice.edu/~andyp 

location  Houston, TX  
age  35  
visits  member for  5 years, 7 months 
seen  8 hours ago  
stats  profile views  14,115 
associate professor at Rice University
1d

comment 
Is there a (satisfying) proof that cellular cohomology is isomorphic to simplicial cohomology that doesn't use relative cohomlogy?
This does not answer the question. 
Apr 29 
awarded  Notable Question 
Apr 27 
awarded  Nice Answer 
Apr 27 
comment 
When a homeomorphism is a diffeomorphism w.r.t to a suitable smooth structure?
@PVAL: Yes, I believe this for involutions, which does give an easier proof (though I think the stuff about the Smith conjecture is useful to show how subtle this kind of stuff is). 
Apr 27 
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When a homeomorphism is a diffeomorphism w.r.t to a suitable smooth structure?
@PVAL: I don't think it is true in general that the fixed point set of a diffeomorphism is a manifold. For instance, I think that there exists a diffeomorphism $f$ of $\mathbb{R}$ whose fixed set is the usual middle third Cantor set (just take the identity function and perturb it on each interval in the complement such that it stays smooth bijective with nonzero derivative and such that the derivative tends towards one on the boundary of the interval). 
Apr 27 
accepted  The word problem for fundamental groups of smooth projective varieties 
Apr 27 
answered  The word problem for fundamental groups of smooth projective varieties 
Apr 27 
revised 
Commutator subgroup of a surface group
added 687 characters in body 
Apr 27 
comment 
When a homeomorphism is a diffeomorphism w.r.t to a suitable smooth structure?
Just to bring out the main theme of my answer, if you fix a smooth structure (as you can in many cases, for instance in low dimensions), you are asking for conditions that ensure that a homeomorphism is topologically conjugate to a diffeomorphism. There is no easy answer to this  it depends in a delicate way on the dynamics of the homeomorphism. For example, the $5$sphere has a unique smooth structure, and I have no idea what possible form an answer to this question would take there. 
Apr 27 
answered  When a homeomorphism is a diffeomorphism w.r.t to a suitable smooth structure? 
Apr 19 
answered  Reference request about the representations of the group $PSL_2(\mathbb{F}_q)$ 
Apr 9 
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What's the minimum amount of knowledge to start doing research?
@StanleyYaoXiao : Yitang Zhang was very aware of (and used) all the relevant technical developments in the subject. He may have been an outsider, but he was hardly a naive amateur. In any case, this is primarily opinion based, so I've voted to close. 
Apr 2 
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Should one post a paper on the arXiv if it is not intended to be published?
You should ask your advisor and do what (s)he says. It is impossible to give advice about this without seeing the paper (and MO is not an appropriate place to ask for evaluations of a paper). 
Apr 1 
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Universal coefficient theorem for group homology and cohomology
@ChrisGerig: As you pointed out in your answer, there is no general theorem. But the result in my answer is a shadow of the UCT that does hold, is often useful, and is not welldocumented in the expository literature. 
Apr 1 
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Universal coefficient theorem for group homology and cohomology
Sorry, I don't have time to type it out (and my copy of the book is at my office anyway; I just copied the reference from one of my old papers which quoted it). His book is pretty standard; I would expect that any university library would have it. 
Mar 31 
answered  Universal coefficient theorem for group homology and cohomology 
Mar 20 
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seminar about the strong multiplicity one for the Selberg class
Presumably it would be more efficient to just ask Ki? 
Mar 20 
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Framed braids and local systems
No. The correct thing to look at is the space $\widehat{X}_n$ of unordered sets $\{(z_1,v_1),\ldots,(z_n,v_n)\}$, where the $z_i$ are distinct points in $\mathbb{C}$ and $v_i$ is a unit tangent vector based at $z_i$ for all $i$. The fundamental group of $\widehat{X}_n$ is the framed braid group, and local systems on $\widehat{X}_n$ yield representations of the framed braid group. 
Mar 20 
awarded  Favorite Question 
Mar 20 
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Algebraic Number Theory in Financial Mathematics
I feel confident that no interesting insights will be found (though perhaps some fools and their money will be separated). Every time some scientific/mathematical theory gets some popular press, bs artists write papers incorporating the relevant buzzwords. In the 70's it was catastrophe theory, then we got chaos theory and fractals, and now I suppose we get string theory. 