20,930 reputation
586162
bio website math.rice.edu/~andyp
location Houston, TX
age 35
visits member for 5 years, 1 month
seen 10 hours ago
associate professor at Rice University

2d
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
Nov
8
awarded  Nice Answer
Nov
8
answered Thurston geometries in dimension 4
Oct
27
awarded  Good Answer
Oct
14
awarded  Yearling
Sep
30
awarded  Explainer
Sep
17
awarded  Notable Question
Aug
31
comment Top specialized journals
@BenoîtKloeckner : They have great ambitions, but I think that at this point they have not reached them (and who knows what will happen when they start charging authors to publish in them).
Aug
25
awarded  Enlightened
Aug
25
awarded  Nice Answer
Aug
24
comment Second homology of mapping class group of genus 3
Thanks Kevin!!!
Aug
24
comment Help with my research topic
While I am sorry you are having trouble, questions of the form "give me a thesis topic" are off-topic and I have voted to close.