All Questions

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Is there any practicable method to determine if the Ω-limts of solutions of dynamical systems exist? [on hold]

Is there any practicable method to determine if the Ω-limts of solutions of dynamical systems exist ?
239 views

Why is every l-adic Galois representation conjugate to one over the l-adic integers? [on hold]

Why is every l-adic Galois representation $$G_{\mathbb{Q}_p}\rightarrow GL_n(\mathbb{Q}_{l})$$ conjugate to one over the l-adic integers? $$G_{\mathbb{Q}_p}\rightarrow GL_n(\mathbb{Z}_{l})$$
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How badly behaved can Lebesgue integrable functions be? [on hold]

Let f be a function in L^1(a, b), with (a, b) a real interval, and : E+ := { x € (a, b): f(x) > 0 } a non-null set, E := { x € (a, b): f(x) = 0 } a null set, E- := { x € (a, b): f(x) < 0 } ...
116 views

Graded structures for simple $C^{*}$ algebras without nontrivial idempotent

Edit: According to the comment of Qiaochu Yuan I realize that $\mathbb{C}^{2}$ is a counter example. So I add the assumption "simplicity" to this edited version Note: In this post, the cyclic ...
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159 views

Is $2^n -1$ finitely many times the product of consecutive primes? [duplicate]

This question was asked at MSE but recieved no attention at all. Here it is: Are there finitely many $(n,k) \in \mathbb{N}^2$ with $2^n-1=p_1p_2\cdots p_k$ ? $p_1=3,p_2=5 , ...,p_k$ are ...
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positions of polyhedrons with vertices on the unit sphere

Let $S^2$ be the unit $2$-sphere canonically embedded in $\mathbb{R}^3$. Let $P$ be a polyhedron whose all vertices are in $S^2$. Let $\text{Iso}(S^2)$ be the isometry group of $S^2$ and ...
125 views

Conditions on the hierarchy for Thurston's hyperbolization theorem

From my understanding the proof of Thurston's hyperbolization theorem for Haken $3$--manifolds consists of cutting the manifold along a hierarchy (collection of incompressible, ...
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Geodesically convex neighborhood in Finsler manifolds

It is well known that every point of a Riemannian manifold $(M,g)$ possesses a fundamental system $\{U_n\}_{n\in\mathbb N}$ of geodesically convex neighborhoods. This means that every pair of points ...
115 views

Idea behind the proof of consistency of club filter of $\omega_1$ is ultrafilter + ZF + DC

I've been trying to understand Radin Forcing and some of its applications, one of which is the use of it to prove the consistency of ''Club filter of $\omega_1$ is an ultrafilter + ZF + DC''. However, ...
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Hilbert transform on boundary value of analytic bounded functions

I am considering the boundary values of a bounded holomorphic functions. Suppose $w$ is a bounded holomorphic function in upper half plane, with continuous and bounded boundary value $f$ on real axis. ...
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Proving compatibility of two Partial differential equations

Given two PDE(s): $F(x,y,z,p,q)=0$ and $G(x,y,z,p,q)=0$ In I.A.N Sneddon's "Elements of Partial Differential Equations",If every solution of $F=0$ is a solution of ...
159 views

Another question on Heath-Brown's “Prime twins and Siegel zeros”

With a graduate student, I'm going through the paper (Proc. London Math. Soc. (3) 47 (1983), no. 2, 193–224.) Here's the background and notation. We have a quadratic character $\chi$ modulo $q$, ...
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+50

Enriching categories and equivalences

Let $\mathcal{C}$ and $\mathcal{D}$ be two equivalent categories. Furthermore, assume $\mathcal{C}$ is enriched over a monoidal category $(\mathcal{M}, \otimes)$. Can one use the equivalence to ...
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+100

Conditions on the fusion data of symmetric fusion category

We know that every symmetric fusion category (SFC) gives rise to data $N^{ij}_k$ that describe the fusion of simple objects: $i\times j = N^{ij}_k k$, and the data $\theta_i =\pm 1$ that describe the ...
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History of spectral methods to the study of real analytic $GL_2$-Eisenstein series

I'm trying to sort out the history of spectral methods in the study of real analytic $GL_2$-Eisenstein series. From what I read so far, I would say that the subject was really kicked off by the ...
162 views

Polynomial differential forms on $BG$

Let $\Omega^{*}_{\text{poly}}\: : \: sSet\to dg_{\geq 0}Comm_{+}$ be the polynomial De Rahm functor on simplicial sets, where the codomain is the category of commutative differential graded algebras ...
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free quotient in Limit groups [on hold]

Let G a limit group. Exist N normal subgroup not trivial of G such that G/N is a free group finitely generated and d(G)=d(G/N)?, where d() is the minimum number of generators of G.
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Perfect matching in a graph [on hold]

Is it true, that in every 2-regular graph with 14 vertices there is a perfect matching ? If you think it's true - prove it, otherwise show counter-example this is my excercise. I think that it's true ...
27 views

Finding equivalent matrix combination [on hold]

I have a program I've written that is solving some problems with some matrix-vector math, but I have a feature I want to add and while I've found a work around an analytic solution would be superior. ...