This tag is used if a reference is needed in a paper or textbook on a specific result.

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Collatz property implying infinite “fall below” trajectories, is it known?

(this was discovered analyzing Collatz empirically.) a key aspect of resolving Collatz involves looking at the number of iterations for trajectories to "fall below" the initial value. consider ...
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0answers
38 views

Connectedness of moduli for topologically trivial rank two bundles on $\mathbb{P}^3$

What is known about connectedness of moduli of vector bundles of rank two, with trivial Chern classes and trivial Atiyah-Rees-$\alpha$-invariant? Ok, this is sort of a delicate question because there ...
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1answer
91 views

Hilbert scheme of an infinitesimal neighborhood of a subvariety

Let $X$ be a complex algebraic variety. Let $C\subset X$ be a compact (reduced) subvariety. Let $C^{(n)}$ denote the $n$th infinitesimal neighborhood of $C$ inside $X$. Let $Hilb(X)$ denote the ...
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1answer
53 views

Minimum of Random Energy Model (REM) with logarithmically correlated potential

In the paper [FB] (ArXiv, J. Phys. A), the authors analyse a particular Random Energy Model (REM) with logarithmically correlated potential and conjecture in Eq. (2) that the distribution function of ...
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0answers
23 views

Uniqueness of Newton (modulo a constant) series on a compact set

Good morning everybody. My question is as follows: Let $K$ be a compact subset of $\mathbb R$ and let $v\in C^\infty(K)$. Consider the finite difference operator $\Delta v(x)\doteq v(x+1)-v(x)$. It ...
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2answers
97 views

Caratheodory equations

Ok, I am reading Fillipov book on discontinuous right hand side differential equations (the red book). He states the next lemma: " Let the function $f(t,x)$ satisfy the Caratheodory conditions and ...
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0answers
50 views

coxeter element of a reflection group (reference request)

I am reading reflection groups and coxeter groups book by Humphreys. now I want to learn more about "coxeter element" of a reflection group. Can any body suggests me some good books to read more about ...
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0answers
46 views

Is the absolute of a compact space the projective limit of the Stone-Čech compactifications of its open dense subsets?

Is the following statement true, and if it is, does someone have a reference? Let $X$ be a compact (i.e., compact and Hausdorff) topological space. Then the Gleason space (=Iliadis absolute, ...
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2answers
216 views

Cohomology of the toric variety $X_\Sigma=\mathbb C^2\sqcup \mathbb C^2\big/\left((x,y)_1\sim(x^{-1},y^{-1})_2\right)_{x,y\neq 0}$

I'm writing a thesis on Chow rings of toric varieties and am looking for a reference on the singular cohomology ring of the blowup of $\mathbb C^2$ at xy=0, i.e. at the coordinate axes. The ...
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0answers
70 views

Action of the (special) orthogonal group on differential forms

I was told that the following facts are true. I am looking for a reference to them. 1) The action of $O(n,\mathbb{C})$ on $\wedge^l\mathbb{C}^n$ is irreducible for any $l$. 2) The action of ...
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56 views

Algebraic subgroup lattices [on hold]

For which groups is the subgroup lattice algebraic? Jiří Tůma has proved every algebraic lattice is an interval in a subgroup lattice. It seems there is close relation between algebraic lattices and ...
3
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0answers
84 views

Birkhoff Ergodic Theorem and Ergodic Decomposition Theorem for Continuous-Time Markov Processes

I have a couple of questions regarding ergodicity for Markov processes in continuous time. (In particular, the first question seems like it should be particularly basic, and yet I haven't managed to ...
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0answers
93 views

First Description of how to Remove Radicals from Equations

Who first described the technique of removing radicals as indicated in the answers to questions Tools for Removing Radicals from Equations and Rewrite sum of radicals equation as polynomial equation ? ...
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0answers
78 views

adjoint representation of 2-Lie groups

Baez and Crans in their paper on Lie 2-algebras refer to adjoint representations of Lie 2-groups but don't say much, as far as I can tell, except to say that such a representation acts on a 2-Lie ...
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0answers
241 views

Reference request: Book of Linear algebra from categorical point of view

Is there any book of Linear algebra in the modern language of Category theory? I refer to the (systematic, formalist) study of the category whose objects are vector spaces and whose morphisms are ...
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1answer
383 views

Learning roadmap to TQFT from a mathematics perspective

I had asked a question on math.stackexchange but did not receive any answers. I hope that this question is appropriate for this website as it is about an advanced subject. Hence I am posting it below. ...
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1answer
125 views

Contracting a planar graph to a (multiply-edged)-tree

Given a planar graph (no loops, no multiple edge), is it always possible to perform edge contractions* in order to obtain a graph $T$ which has no loops, but if one forgets the multiplicity of its ...
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0answers
90 views

Star shaped sets with a midpoint

Suppose $U$ is an open subset of $\mathbb{R}^n$ which is star shaped with respect to $p\in U$. I'll call $p$ a midpoint of $U$ if for any line $\ell$ through $p$, the point $p$ is the midpoint of the ...
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1answer
130 views

Does the “Ohsawa-Takegoshi theorem without bounds” have a name?

There are many theorems which now could be called "The Ohsawa-Takegoshi" theorem. Of these, the most basic is roughly the following: Let $\Omega \subset \subset \mathbb{C}^n$ be a psuedoconvex ...
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2answers
221 views

Embed one Coxeter System into another

What is a good reference that explains all the braid relations and diagrams for Coxeter systems concisely? In particular, how do I embed $H_3$ inside $D_6$, or $H_4$ inside $E_8$? Any hints?
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1answer
103 views

Levenberg's original article “A method for the solution of certain problems in least squares”

Does there exist any digital copy of the original article (or a transcript) K. Levenberg, A method for the solution of certain problems in least-squares, Quart. Appl. Math. 2 (1944): 164-168? It is ...
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1answer
264 views

Does OCA imply $2^{\aleph_0}=\aleph_2$?

Is it known whether Todorcevic's Open Coloring Axiom implies $2^{\aleph_0}=\aleph_2$? The only consistency proofs for OCA that I know are the following: 1) PFA implies OCA (and also ...
4
votes
1answer
80 views

Equations and random subgroups in compact groups

Let $G$ be a compact group (I am mainly interested in the profinite case). Pick a sequence of $d$ elements (where $d$ is either finite or $\omega$) independently at random (w.r.t. Haar measure) and ...
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1answer
165 views

Vanishing of Motivic Cohomology

In these notes, page $10$, bullet $(5)$, it is stated that if $X$ is a scheme of finite type over a field $k$, then the motivic cohomology $\mathrm{H}^{p,q}(X,R)$ of $X$ over $k$, where $R$ is a ring, ...
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60 views

Reference request: How you can reach any point in the vector space of vector fields generated by Lie brackets

By a Theorem of Chow, you can reach any point in the vector space of vector fields generated by Lie brackets. Do you know any reference for this theorem?
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1answer
208 views

Relationship between fragments of the axiom of choice and the dependent choice principles

The dependent choice principle ${\rm DC}_\kappa$ states that if $S$ is a nonempty set and $R$ is a binary relation such that for every $s\in S^{\lt\kappa}$, there is $x\in S$ with $sRx$, then there ...
3
votes
2answers
325 views

Zigzags and contractibility of categories

Let $\mathbf{C}$ be a small category and $\mathbf{C}'$ its hammock localization in the sense of Dwyer and Kan. I am looking for a proof (or counterexample) of the following assertion: If there is ...
8
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1answer
201 views

Integers with a large prime divisor in short intervals

For an integer $n$, denote by $P^+(n)$ the largest prime divisor of $n$. Then we have the following: There exists some $c>0$, such that for all $x$ sufficiently large the number of integers ...
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0answers
64 views

Linkage between homotopy equivalence and identification of algorithms

I vaguely recall that someone says there is linkage between homotopy equivalence and identification of algorithms which may be isomorphic or morphism or something like that,the algorithm may be ...
2
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2answers
127 views

How to define the input of computable function or Turing machine over real numbers

Computation or computability over $\mathbb{N}$ can be extended to computation or computability over $\mathbb{R}$ or even computation or computability over $\mathbb{C}$.The following is a formal ...
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1answer
67 views

A Modified Birkhoff-von Neumann Theorem [closed]

Sorry for having two open MO posts. Let "stochastic" matrix be the matrix whose rows sum to one and deterministic matrix be a stochastic matrix whose all rows consist of a one and zero. For example ...
2
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0answers
33 views

Reference request: Edmond's Algorithm for integer hull

I'm looking for a good reference for the algorithm (supposedly by Edmonds) to compute the integer hull of a polytope, not by cutting plane methods but by starting with a set of integer points and then ...
4
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0answers
99 views

Nontransitive dice

In the wikipedia article https://en.wikipedia.org/wiki/Nontransitive_dice it is claimed that " The set of nontransitive dice were investigated by the Latvian computer scientist and mathematician ...
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1answer
68 views

On Severi's definition of the complementary correspondence

In Weil's short note entitled "On the Riemann hypothesis in function-fields" he mentions the notion of the complementary correspondence associated to a given correspondence $T:C\rightarrow C$ where ...
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55 views

Property of set of prime numbers [migrated]

let $\{p_1,p_2,p_2,\cdots ,p_r\}$ be the set of $r$($\ge2$) pair wise distinct prime numbers i.e.., $(i\ne j \implies p_i \ne p_j)$ for all $1\le i,j\le r$ ${Statement}$ : For any such ...
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0answers
76 views

The 'most general' papers on rational Borel-Moore motivic homology and K'-theory?

There are two ways to define Borel-Moore motivic homology (of schemes) with rational coefficients: one should either consider certain complexes of algebraic cycles, or the $\gamma$-filtrations of ...
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1answer
131 views

Conjectured Primality Test for Numbers of the Form k2^n+1 with n>2 [closed]

Definition : Let $P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^m+\left(x+\sqrt{x^2-4}\right)^m\right) $ where $m$ and $x$ are positive integers . Conjecture : Let $N=k\cdot 2^n+1$ with ...
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0answers
137 views

Two Definitions of Non-commutative $L^p$ space

Throughout, let $(\mathcal{M},\tau)$ be a von Neumann algebra $\mathcal{M}$, acting on a Hilbert space $H$, with normal semifinite faithful trace $\tau$. In the survey article by Pisier and Xu, the ...
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1answer
202 views

vanishing higher cohomology group for property T group?

Given a countable discrete group $G$ with Kazhdan's property (T), consider $\mathbb{C}G$ or $l^2(G)$ as a left $G$-module, then we can consider the group cohomology, Is it known that $H^n(G, ...
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1answer
290 views

Is there any current development of a first order formalization of metamathematics?

I hope that this post isn't off topic, but I already asked math.stackexchange about first order formalizations of first order logic. There are provability logics and extensions in modal logic's that ...
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1answer
163 views

Atkin--Lehner operators in Hida theory

Let $p$ be a prime, and $F$ a $p$-adic Hida family of ordinary modular forms (of some tame level $N \ge 1$). I'd like to know whether, for $q$ a prime factor of $N$, the actions of the Atkin--Lehner ...
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0answers
76 views

(Homotopy) limits and colimits in a dg-category

It is known that differential graded categories (or, also, $A_\infty$-categories) are 'incarnations', in some sense, of (stable) $(\infty,1)$-categories. I'm not used to the theory of ...
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0answers
162 views

K-theory of $\mathbb{RP}^\infty$

can anyone give some reference of K-theory and K-homology of $\mathbb{RP}^\infty$, both $K_0$ and $K_1$. PS: also posted in stackexchange
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1answer
157 views

Reference request: Deligne's conjecture (cycles)

In "The work of Tate" Milne says: "The relation between the two conjectures has been greatly clarified by the work of Deligne. He defines the notion of an absolute Hodge class on a (complete ...
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1answer
229 views

Reference request: Grothendieck´s period conjecture?

I would like to know if Grothendieck published something about this conjecture? Is there some book (or expository article) about this conjecture? Is there any connection between this conjecture and ...
8
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1answer
420 views

Rank of Elliptic Curves

Recently, I have heard of some heuristics that would suggest that the rank of elliptic curves are bounded (specifically in the congruent number family). I always though that the best way to prove ...
14
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1answer
714 views

Is $x^{n}-x-1$ irreducible?

Is it true that for every $n \in \mathbb{N}$, $x^{n}-x-1$ is irreducible in $\mathbb{Z}[x]$? The standard irreducibility criteria seem to fail.
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0answers
112 views

Rewrite sum of radicals equation as polynomial equation

My question is about a method described in Dr.Math forum for simplifying equations involving sums of radical functions. (The following is a transcription of the example given by Dr. Vogler): --- ...
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0answers
69 views

Stokes operator without dirichlet boundary condition

Let $\Omega$ be a domain, then the following stokes operator is quite well known : $\mathcal{H} \rightarrow \mathcal{V}_{\sigma} $ $f \rightarrow u$ such that $ - \Delta u = f $ where $ ...
4
votes
1answer
465 views

3n+1 problem and cycles

Just to make sure I am up to date with this problem. I know (or I think I do) that it is not yet proven that there are no non-trivial cycles for the collatz sequence (please correct me if I am wrong). ...