20,960 reputation
587162
bio website math.rice.edu/~andyp
location Houston, TX
age 35
visits member for 5 years, 2 months
seen 3 hours ago
associate professor at Rice University

5h
comment Can the divisibility-by-7 test be extended to preserve the remainder?
MO is intended for questions at the mathematics PhD student level and above. I've voted to close.
2d
accepted Torsion in GL_n(Z)
2d
comment calculate the norm of operator
MO is not for homework. I've voted to close.
Dec
22
comment Two problems in functional analysis
MO is not for homework. I've voted to close.
Dec
22
comment Is there a “good” reason that the universal central extension of $SL(2,\mathbb Z)$ is $Br_3$?
There's an elegant discussion of this on pages 83-85 of Milnor's book on algebraic k-theory.
Dec
19
comment transition matrix
MO is not for homework and is for questions at the mathematics PhD student level and above. I've voted to close.
Dec
14
comment Good Pre-Calculus book?
While I'm glad you want to learn math more deeply, that website misled you -- MathOverflow is intended for questions at the mathematics PhD student level and above, so your question is off-topic. I recommend that you check out math.stackexchange.com, which welcomes questions at all levels.
Dec
9
comment What is wrong with the “naive” proof of the Hauptvermutung?
I think there is no way to do this in the topological category. You're going to have to first prove that topological surfaces can be given PL or smooth structures. Once you have that, you can use PL or smooth triangulations and apply transversality to make an argument like you propose go through.
Dec
4
accepted Making the branching rule for the symmetric group concrete
Nov
30
awarded  Notable Question
Nov
29
comment The resolution of which conjecture/problem would advance Mathematics the most?
I feel that this question is too broad and unfocused, as well as being too "opinion-based".
Nov
24
comment Counting Ribbon graphs
@Cusp: The data is redundant since $e = vd/2$. If you want isomorphism classes, this seems impossible (in the moral, not the technical sense) for the same reason that it is impossible to write down a closed formula for the number of isomorphism classes of degree $d$ graphs with $v$ vertices.
Nov
23
comment Koebe–Andreev–Thurston theorem - where can I find a proof?
nb: As an illustration of the connection to conformal geometry, you can construct circle packing of the disc from any planar graph; the "exterior" circles are all tangent to the exterior circle. The different possible unit disc circle packings realizing a given planar graph then differ by Mobius transformations.
Nov
23
comment Koebe–Andreev–Thurston theorem - where can I find a proof?
@AllenKnutson: I'm not familiar with the term "coin graphs", but the circle packing theorem as stated in the question is quite old (it basically goes back to Koebe, though it has been rediscovered several times). My guess is that this is simply a matter of two communities of people not talking to each other. The various proofs of the circle packing theorem that I know are not really combinatorial. As Thurston taught us, constructing a circle packing is very similar to constructing a conformal map, so it does not surprise me that the graph theory community has not managed to prove it.
Nov
22
comment Koebe–Andreev–Thurston theorem - where can I find a proof?
A proof can be found in Stephenson's lovely book "Introduction to Circle Packing: The Theory of Discrete Analytic Functions".
Nov
20
awarded  Enlightened
Nov
20
awarded  Nice Answer
Nov
16
comment Two (other) rings…are they isomorphic?
@WłodzimierzHolsztyński: While of course one can overdo this, I think that what the OP does here is totally fine, and I see no reason to criticize him for it (implicitly or otherwise).
Nov
11
comment Synthetic vs. classical differential geometry
I think that most mainstream work in Riemannian geometry ignores SDG. Though I'm only on the boundary of Riemannian geometry, my impression is that there really isn't a "foundational crisis". The biggest issues are related to things where category theory is mostly pretty useless, like analysis.
Nov
8
awarded  Enlightened