21,890 reputation
591166
bio website math.rice.edu/~andyp
location Houston, TX
age 35
visits member for 5 years, 7 months
seen 8 hours ago
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
comment 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
comment 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
comment 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
comment 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 well-documented in the expository literature.
Apr
1
comment 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
comment seminar about the strong multiplicity one for the Selberg class
Presumably it would be more efficient to just ask Ki?
Mar
20
comment 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
comment 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.