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Feb
6
comment Properties of nerve of strict n-groupoid
Why has this answer been downvoted??
Feb
3
comment How many simplicial complexes on n vertices up to homotopy equivalence?
I understand why the number of labelled and unlabelled complexes on $n$ vertices differs by the $n!$ factor of course, but it is not clear why counting up to homotopy shouldn't make a bigger difference than that factor.
Jan
27
revised Kirillov orbit Method for Complex nilpotent groups
Title spelling
Jan
20
awarded  Popular Question
Jan
18
reviewed Approve Expectation of a specific random variable on the probability space of $n\times n$ matrices over $\{0,1\}$
Jan
18
reviewed Approve Is a “knot knot” or “double knot” a thing in knot theory?
Jan
18
reviewed Approve Cross section point of two conics curves
Jan
2
revised How is Ricci flow related to computer graphics?
You're welcome, Deane.
Dec
22
comment If presheaf is zero on a covering is the sheaf zero?
From the last line, it follows that the colimit of every system of vector spaces is zero.
Dec
17
comment classifying space of G-invariant function
The quick answer to your first question is "no", at least if the question is interpreted in its most naïve form: CJS build a top-enriched category F whose objects are the critical cells and the hom-spaces F(x,y) are derived from the moduli space of reparametrized broken flow lines. If you follow their construction, there is no reason (at least, none I can see) why each F(x,y) should inherit the group action. I think you can make a very compelling case when the hom spaces are also equivariant: eg when rotating a sphere about the north-south diameter...
Dec
12
comment On Sampling rank $r$ matrices
@kodlu I think it is pretty clear what is being asked. Q1: given $n^2$ integer of absolute value smaller than $d$, what are the odds that the matrix they generate has rank $r$? And Q2, what is an efficient algorithm for uniformly sampling from the set of $n \times n$ matrices with entries < $d$ and rank $r$? Deterministic only means that the algorithm should not be probabilistic in the sense of giving the right answer only with probability $> 1 - \epsilon$ for a priori choice of $\epsilon$.
Dec
11
comment Open Problems for Undergraduates
Think about the constraints you are placing on this hypothetical problem list: the problems should be interesting enough for someone to collect and easy enough for an undergrad to solve, either too new or too obscure to be "long-standing", but miraculously not already solved by the people who collect such problems. I'm not saying no such list can exist, but I'd be surprised if it did. In any case, let me strongly recommend that you apply for a summer REU --- those are designed precisely for the sort of people you appear to be describing.
Dec
7
comment f vectors of simplicial complexes homeomorphic to n dimensional spheres
For a triangulated manifold of dimension $d > 0$, the $(d-1)$-dimensional simplices must all have exactly two $d$-dimensional co-faces.
Dec
6
awarded  Popular Question
Dec
5
comment Topology of categories, very basic facts surrounding Quillen's Higher Algebraic K-Theory I
Your first claim is akin to saying that the study of maps from a given space $X$ to the real line carries no interesting topological information because $\mathbb{R}$ is contractible. In particular, this would make all of Morse theory useless... The advantage of that result is an ability to compare (pre)sheaves taking values in categories which you seem to care about (like Set, Top and Vect)
Nov
13
comment Bi-adjointness and isomorphisms of (co)limits
@QiaochuYuan fantastic, thanks! If you make that comment into an answer, I'll gladly accept.
Nov
13
revised Inference using Topological Data Analysis: Is it worth it for a regular statistician to learn TDA?
Otter link
Nov
12
asked Bi-adjointness and isomorphisms of (co)limits
Nov
9
comment What are some very important papers published in non-top journals?
I think what @gowers means is that "math. ann." does not commute.
Nov
2
comment Terminology for vanishing of Hochschild homology with symmetric coefficients?
I don't have an answer, but +1 for wanting to change that title. For what it is worth, it is entirely reasonable to say $A$ is $n$-acyclic with $M$-coefficients if $H_k(X;M) = 0$ for all $k \geq n$. So maybe "2-acyclicity of a commutative Banach algebra in Hochschild homology with symmetric coefficients"?