21,504 reputation
590165
bio website math.rice.edu/~andyp
location Houston, TX
age 35
visits member for 5 years, 5 months
seen 1 hour ago
associate professor at Rice University

2d
comment Math mobile Apps
MO is intended for questions at the mathematics PhD level and above. I've voted to close.
2d
comment Problems concerning meromorphic 1 form on Riemann surface
MO is not for homework.
Mar
24
comment Probability or odds of something happening
MO is intended for questions at the mathematics PhD level and above. I've voted to close.
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 $\mathbb{R}^n$.
Mar
18
awarded  Good Answer
Mar
14
comment Parodies of abstruse mathematical writing
@ToddTrimble: Wildberger has rather extreme and idiosyncratic views about a supposed lack of rigor in contemporary mathematics. I think the hostility you see is a reaction to the fact that few mathematicians take him very seriously.
Mar
9
comment Decision problem on triviality of intersection of two subgroups
It is not decidable in general since it would allow you to solve the word problem (given an element $w$, just apply it to the subgroups $\langle w \rangle$ and $\langle w \rangle$; their intersection is trivial if and only if $w$ is trivial). On the other hand, it is decidable for free groups; indeed, using the algorithm described in Stallings's paper "The topology of finite graphs", you can compute the rank of the intersection of two finitely generated subgroups of a free group.
Feb
27
answered Computation of homotopy groups of spheres via Pontryagin-Thom
Feb
27
answered Maps with Hopf invariant zero are suspensions
Feb
20
awarded  Nice Answer