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Vidit Nanda

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Name Vidit Nanda
Member for 1 year
Seen 2 hours ago
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Location New Jersey
Age 30

Formerly Vel Nias

math genealogy
1d
 comment What fraction of n-point sets in the unit ball have diameter 1?
Thanks for this, Ricardo. I am still parsing your answer, I'll get back to you once I understand this.
Jun
14
 revised What fraction of n-point sets in the unit ball have diameter 1?
added two mathcals to avoid duplicate notation for B
Jun
14
 comment Can we invert barycentric subdivision?
Thanks a ton, Ricardo. I have accepted your answer for now so that my question doesn't keep getting popped to the front page. I hope you will understand if I undo this acceptance in the event of a more precise answer from you or someone else.
Jun
14
 asked What fraction of n-point sets in the unit ball have diameter 1?
Jun
2
 comment Can we invert barycentric subdivision?
Ricardo: I think you should post this as an answer because it is as close as we are likely to get to one. I will accept so that this question doesn't keep appearing on the front page. This has the added benefit of tormenting residential skeptic Ryan :)
Jun
2
 comment Can we invert barycentric subdivision?
thank you for the reference, Ricardo. It is a strange characterization: no 1-manifolds, no simplices and no boundaries of simplices!!??
May
31
 revised Can we invert barycentric subdivision?
added 183 characters in body; added 73 characters in body
May
31
 comment Can we invert barycentric subdivision?
Fernando: thanks for this reference! Ryan: see Fernando's link, it contradicts what you appear to be saying. Henr: doesn't an affirmative answer to 3 force an affirmative answer to 1?
May
31
 asked Can we invert barycentric subdivision?
May
29
 comment Biggest ball included in an intersection of balls
Regarding the first (okay, second) sentence: assume $d = 2$. Certainly, we can construct $4$ balls whose intersection contains all the centers, but so that the intersection of any $3$ is strictly larger than the intersection of all $4$. Therefore, the largest ball which fits into the intersection of $3$ will almost surely not fit into the intersection of all $4$. How can we use Helly's theorem to just restrict attention to $d+1$ balls??
May
28
 comment A notion of a ‘coarse’, parametrized dimension of an object, where the parameter determines how finely we can distinguish (say) a very thin rod from a line
ithmath, that's about right. Of course, the map $f: M \to |K|$ from the definition need not be a "contraction" in the strict sense (of strong deformation retraction): it is just any continuous map with control on sizes of point inverses. And yes, the fact that you can construct a triple $(K,f,\epsilon)$ for some choice of $n$ only tells you that the macroscopic dimension is $\leq n$ at your scale $\epsilon$.
May
27
 accepted A notion of a ‘coarse’, parametrized dimension of an object, where the parameter determines how finely we can distinguish (say) a very thin rod from a line
May
27
 answered A notion of a ‘coarse’, parametrized dimension of an object, where the parameter determines how finely we can distinguish (say) a very thin rod from a line
May
23
 answered How many triangulations of the genus $g$ surface on $n$ vertices?
May
22
 comment Does this qualify as “self plagiarism” or something?
If all your work is in one sub-field, it would be surprising to not see isomorphic background sections for all your papers. It's only cause for concern if you are claiming a new contribution each time or something, which does not sound like the case. I would recommend citing some of your earlier papers along with other related material at the outset of your latest background section, with a sentence like "the following definitions and results are similar to those in [5,6,8,12,16]"
May
20
 comment Finitely generated monoids are finitely presented?
Why is this an answer instead of an up-vote of Tom Church's comment from... 3 years ago?
May
13
 comment “monotone” homotopy?
What is "the" Hausdorff axiom? What does your ncatlab link have to do with that axiom? What do the axiom and this link have to do with the original problem?
May
13
 comment “monotone” homotopy?
I have not seen this before, but you may be interested in looking up "controlled homotopy theory".
May
5
 revised Category with a “metric” for arrow composition
Yet another unbalanced parenthesis :(
May
4
 awarded ● Nice Question
Apr
30
 comment Uniqueness of fixed points for rational transformations
You want to know if $T\circ T$ has a unique fixed point. If $T$ fails to have a unique fixed point (it must have at least one) then the search is hopeless. So, my question was: have you made any progress on solving the much easier-looking problem: does $T$ have a single fixed point?
Apr
30
 comment Uniqueness of fixed points for rational transformations
Isn't every fixed point of $T$ also a fixed point of $T\circ T$? Why not just ask about uniqueness of the fixed point of $T$ (which must also exist by Brouwer's theorem)?
Apr
29
 awarded ● Citizen Patrol
Apr
24
 awarded ● Nice Answer
Apr
22
 comment Transformation between Left and Right Kan Extensions
Andreas, should be fixed now I think. Michal, thank you for commenting but I am unfamiliar with your notation: what are those integral signs?
Apr
22
 revised Transformation between Left and Right Kan Extensions
addressed errors, etc pointed out in comments
Apr
22
 asked Transformation between Left and Right Kan Extensions
Apr
20
 comment Is this a Banach space?
What is $x$ in the definition of $X$?
Apr
20
 awarded ● Nice Question
Apr
11
 comment Hall’s Marriage Theorem and intervals
I haven't seen this generalization before, but you should make sure it doesn't follow obviously from something like exercise III.4.6 in Bourbaki's set theory (I don't think it does, but it's too early in the morning).
Apr
11
 comment Fixed point theorems
For a finite $S$ it is presumably easier to count the fixed points of $f$ "by hand". Of course, this old-school method doesn't quite give you Burnside's Lemma...
Apr
10
 awarded ● Nice Answer
Apr
10
 revised Fixed point theorems
added homotopy invariance
Apr
10
 revised Fixed point theorems
Added Heitsch survey
Apr
10
 answered Fixed point theorems
Apr
10
 accepted Testing simplicial complexes for shellability
Apr
10
 answered Testing simplicial complexes for shellability
Apr
8
 comment Is the space of diffeomorphisms homotopy equivalent to a CW-complex?
Peter: thank you for addressing the compact open topology. Also, +1 for "horrendibly".
Apr
8
 comment Is the space of diffeomorphisms homotopy equivalent to a CW-complex?
Peter, isn't the Whitney topology very different from the compact-open topology which Ricardo is asking about?
Apr
7
 accepted Combinatorial distance between simplicial complexes
Apr
6
 comment Combinatorial distance between simplicial complexes
Wlodzimiers, the vertex labels in the drawing are not part of the input data. Basically, you have no idea when one simplex that you would like to remove from $K_1$ is actually isomorphic to another simplex from $K_2$ or not without already knowing the space of all partial simplicial maps $K_1 \to K_2$. To convince yourself that the problem is indeed computationally hard, start with Joseph's picture but remove all the vertex labelings!
Apr
5
 comment Combinatorial distance between simplicial complexes
Joseph, I am now confused about the calculation in your example. What happened to the 2-simplex $cef$ which is present in $K_2$ but not in $K_1$, but did not contribute to the distance?
Apr
5
 answered Combinatorial distance between simplicial complexes
Apr
4
 comment Extending simplicial complex to a manifold
What do you mean when you say "a simplicial complex contained in $S$"? Do you mean $|X|$ can be embedded into $S$?
Apr
4
 comment Homotopy equvalence from contractibility of fiber.
Andy: this is how I have seen (and stated) this theorem also, but does one really need to say "surjective"? The empty set does not have the homotopy type of a point, does it?
Apr
1
 comment Does the metric space of compact metric spaces satisfy the binary intersection property?
Thanks, Vladimir!
Mar
20
 comment Is there a general theory of fiber theorems?
Ricardo, I'm definitely going to take a look at Lacher's paper. Thank you again.
Mar
19
 comment Is there a general theory of fiber theorems?
Thanks! This definitely answers the concrete question!
Mar
19
 awarded ● Nice Question
Mar
19
 comment Algebraic Morse theory
@Leon: no worries, glad to help. I wasn't kidding in my answer, it is really cool to see people (especially grad students) seriously studying algebraic or discrete Morse theory!