21,583 reputation
590165
bio website math.rice.edu/~andyp
location Houston, TX
age 35
visits member for 5 years, 6 months
seen 4 hours ago
associate professor at Rice University

2d
comment Are Modular Collatz Graphs strongly connected?
I'm not going to get in an argument with you about this. But MO is intended for questions at the mathematics PhD student level and above. Checking a proof like that is not at this level. I will not respond further.
2d
comment Are Modular Collatz Graphs strongly connected?
(also, famous open problems with elementary statements attract tons of cranks, so the bar for questions about them is higher than usual)
2d
comment Are Modular Collatz Graphs strongly connected?
If you are not mathematically sophisticated enough to check a short proof using nothing but elementary number theory, then MO is not the right website for you. I doubt it would be a good question even if you did not have a purported proof (but I haven't thought hard about it), but the fact that you've already been given one muddies the waters enough that it's a bad question.
2d
comment Are Modular Collatz Graphs strongly connected?
MO is not intended for checking proofs. I've voted to close.
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.
Mar
19
comment cohomology of the orbit space of a group action
@MarkGrant : It's definitely true if $|G|$ is invertible in $F$ (with the same proof). As for whether the isomorphisms respect cup products, I rather doubt it, though I don't have an example in mind. If $G$ acts freely (so the projection $M \rightarrow M/G$ is a covering map), then the isomorphism is induced by the transfer map. See the answer to mathoverflow.net/questions/58159/… for an example of where this is not a ring homomorphism (though that example is not over a field of characteristic $0$).
Mar
19
comment Algebraic Number Theory in Financial Mathematics
I'm pretty skeptical of these purported "connections" between financial markets and particle physics.
Mar
19
revised Ivanov's metaconjecture on surface homeomorphisms.
added 1117 characters in body
Mar
19
answered Ivanov's metaconjecture on surface homeomorphisms.
Mar
19
answered cohomology of the orbit space of a group action
Mar
18
comment Riemannian simplicial complex and quasi-conformal complex
Yes, I believe that is correct.
Mar
18
comment Riemannian simplicial complex and quasi-conformal complex
Robert is talking about the metric properties of these complexes; the rigidity he refers to comes from endowing each simplex with the metric coming from the standard simplex in $\mathbb{R}^n$.