Newest Questions
162,007 questions
6
votes
1
answer
141
views
Circle action on free loop space of a classifying space
It is a folklore result that if $G$ is a discrete group and $BG$ its classifying space, then the free loop space $L(BG)$ is homotopy equivalent to $EG\times_{Ad} G$ where $EG$ is the universal $G$-...
- 113
3
votes
1
answer
130
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A structured recursive formula for the complete homogeneous symmetric polynomial
I recently discovered a recursive, closed-form summation formula that appears to compute the complete homogeneous symmetric polynomial $h_n(x_0, x_1, \dots, x_{m-1})$, but in a more structured and ...
- 39
0
votes
0
answers
36
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From global to local: strong failure of regularity (quasirandomness) in random bipartite graphs
Let $n$ be a positive integer and $\varepsilon > 0$ with $\varepsilon \ll 1$ and $n \gg 1/\varepsilon$. Let $G = (A, B, E)$ be a bipartite random graph with $|A| = |B| = n$, where each edge between ...
- 379
0
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0
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56
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Fejér-Riesz inequality for $H^p$ on the unit disk for more general curves
Let us consider the Hardy space $H_p$ on the unit disk, and a function $f \in H_p$. There's an inequality by Fejér and Riesz stating that:
\begin{equation}
\int_{-1}^{1} |f(x)|^p \, dx \leq \frac{1}{2}...
1
vote
0
answers
58
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Projective module over Robba ring
Is a projective module finitely generated over Robba ring free?
-2
votes
0
answers
49
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Can we have a descending powerset class in Stratified ZF?
Working in $\sf Stratified \ ZF + Class \ Comprehension$, where class comprehension is that of Morse-Kelley. Is there anything to forbid having a class $C$ that meet these two conditions:
$\forall x \...
- 12.4k
-1
votes
0
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22
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Sigma Algebra- All of Statistics [migrated]
I am reading the book All of Statistics by Larry Wasserman. In the first chapter he defines probability axioms and says that it is not always possible to assign probabilities to all the subsets of a ...
6
votes
0
answers
95
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Is there a model category structure for C-homotopy?
After reading Harry Altman's question about homotopy with regards to arbitrary connected spaces I started wondering about the extent to which the notion defined there is compatible with more recent ...
- 15.7k
0
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0
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43
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What do invariant subspaces of graph-related matrices encode?
The question that I have posted here is as follows:
The eigenvalues of the adjacency matrix or laplacian matrix for a given graph $G$ has been relatively well studied. These provide a rather ...
- 179
1
vote
0
answers
60
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Ordinary Quivers for Infinite-Dimensional Algebras
I am wondering if there is an analogue to the ordinary quiver for a finite-dimensional, basic, connected $\Bbb K$-algebra. In particular, I am interested in an ordinary quiver for the polynomial ring $...
- 11
0
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0
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50
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Maximal density of overlapping circle packing
I'm looking for a way to prove that on a plane if we place points with a minimal distance of $d$ and each point is the center of a circle of radius $d$ then the density of the plane is no more than $\...
- 1
0
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0
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43
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When is −∥x−y∥+∥A(x−y)∥ a CPD kernel ? - Difference of CPD radial kernels remains CPD (Bernstein functions)
I’m studying a family of translation-invariant kernels built from two norms and would like to understand exactly when their difference remains conditionally positive-definite. In particular, we focus ...
- 1
0
votes
0
answers
23
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Uniform entropy bounds for unions of VC subgraph classes
I'm working with VC subgraph classes of functions, say $\mathcal{F}$ and $\mathcal{G}$, which are both uniformly bounded and admit envelopes $F$ and $G$, respectively. I came across a useful lemma (...
- 125
1
vote
0
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178
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Periodic cyclic homology and Hochschild homology
Suppose we have a quasi-compact quasi-separated scheme $X$ and consider $D_{QCoh}(X)$ the dg enhancement of derived category of quasi coherent sheaves on $X$. Then the Hochshild Homology $HH_*(X)$ is ...
- 481
2
votes
1
answer
195
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Endomorphisms of groups schemes involving $\mathbb{G}_a$ and flat base change
Let $R$ be a ring of positive characteristic. Let $G$ be a commutative affine and smooth group scheme over $R$. I consider two abelian groups:
$$M(G):=\mathrm{Hom}(G,\mathbb{G}_{a,R})$$
and
$$N(G):=\...
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