Questions tagged [reference-request]
This tag is used if a reference is needed in a paper or textbook on a specific result.
9,216 questions
0
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0answers
14 views
Sufficient condition for the absolute convergence of Fourier series of a function on the adele quotient $\mathbb A_k/k$
Let $G$ be a compact abelian group. The unitary characters of $G$ form an orthonormal basis of $L^2(G)$, so every square integrable function $f: G \rightarrow \mathbb C$ admits a Fourier expansion
$$...
3
votes
1answer
76 views
Partition Calculus and Ramsey theory question
These topics are outside of my area of research, so I am not quite sure where in the literature to find the answers.
In what follows, if $X$ is partially ordered and $n$ is a natural number, let $[[...
5
votes
1answer
159 views
Sheaves over a sheaf
Everything I write I mean in the in the sense of Lurie's HTT.
Suppose that $ \mathcal{C}$ be a site and let $ F \in Fun( \mathcal{C}^{op} , \mathcal{S})$. Is it always/ever true that $ Sh(\mathcal{C}...
-1
votes
1answer
98 views
If $p_n(a,b)$ is a rational number (or integer) for 3 consecutive values of $n$ then every $p_n(a,b)$ is
Let $a$ and $b$ be two real numbers and $p_n(x,y)$ the polynomial: $$p_n(x,y)=\sum_{i=0}^{n-1}x^{n-1-i}y^{i},$$ where $n$ is a positive integer.
In a previous post I asked if $p_n(a,b)$ was a ...
5
votes
1answer
146 views
One particle irreducible Feynman diagrams
In quantum field theory Feynman has invented a diagrammatic method to encode various terms in the Taylor decomposition of integrals of the following form below which I will write in a baby version as ...
9
votes
0answers
103 views
Quantum Hamiltonian reduction and Quantum Airy structure
I have been reading Kontsevich and Soibelman's "Airy structures and symplectic geometry of topological recursion" (https://arxiv.org/pdf/1701.09137.pdf) and having trouble understanding their Section ...
24
votes
1answer
576 views
Littlewood’s three precepts of refereeing in mathematics: is it (1) new, (2) correct, (3) interesting?
I have a question regarding Littlewood’s three precepts of refereeing a mathematical paper, namely whether it is (1) new, (2) correct, and (3) interesting.
I have found these mentioned in the ...
0
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0answers
97 views
+300
Continuity of Intersection Pairing on Chow monoids
Let $X$ be a smooth irreducible complex projective variety. As we know, if $\alpha,\beta$ are two cycles intersecting properly in $X$, we can define, via Serre's Intersection Formula, their ...
3
votes
0answers
49 views
smoothness of Hurwitz spaces with arbitrary ramification profiles
Fix integers $n\ge 3,d\ge 2$, and partitions $\lambda_1,\ldots,\lambda_n$ of $d$. Let $\mathcal{H}$ be the moduli space of degree $d$ covers $f:C\to\mathbb{P}^1$ that have ramification profiles $\...
2
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0answers
39 views
Holomorphic Poisson structures on $C P^{n-1}$ and homogeneous Poisson structures on $C^n$
Is it correct that any holomorphic Poisson structure on $C P^{n-1}$ can be lifted to a homogeneous Poisson structure on $C^n$? By homogeneous I mean a quadratic Poisson structure of the form $\{z_i,...
1
vote
1answer
52 views
Name of a function space
For a real function $f$ on $\mathbb{R}$, define $e_n(f)$ to be the infimum of the $L_1$ distance between $f$ and piecewise constant functions on the subdivision of $\mathbb{R}$ into intervals of ...
2
votes
1answer
96 views
Local Sobolev embedding on complete Riemannian manifold
Let $(M,g)$ be a complete Riemannian $m$-manifold, with bounded geometry and $m\geq2$. Suppose $Ric\geq(n-1)\kappa$. Let $B_p(r)$ be a geodesic open ball.
Q Can we find a constant $C=C(\kappa,r,m)$(...
1
vote
0answers
42 views
The Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_3$-extension of $\mathbb{Q}(\sqrt{-3})$
I'm now on a research about the Iwasawa $\lambda$-invariants of the cyclotomic $\mathbb{Z}_p$-extensions of number fields. And it happens that the cyclotomic $\mathbb{Z}_3$-extension of $\mathbb{Q}(\...
0
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0answers
19 views
Reference request: Numerical methods for Hamilton-Jacobi-Bellman equations with state constraints
I have two questions on numerical methods for solving Hamilton-Jacobi-Bellman (HJB) equations with state constraints.
Consider an optimal control problem given by
$$
v(x) = \max_{\{u(t)\}_t} \int_o^\...
2
votes
1answer
114 views
Fixed points of the automorphisms of sporadic groups
Sporadic groups have very few outer automorphisms (in fact, $|\mathrm{Out}(G)|\leqslant2$), so it is very natural to ask what are the fixed points subgroups. For a group of Lie type (and a suitable ...
11
votes
1answer
236 views
Are there nice isomorphisms $\operatorname{S}^2(k^n)\cong\Lambda^2(k^{n+1})$?
This might be forced to migrate to math.SE but let me still risk it.
The spaces $\operatorname{S}^2(k^n)$ and $\Lambda^2(k^{n+1})$ from the title have equal dimensions. Is there a natural isomorphism ...
-3
votes
0answers
68 views
Power of an integer as a sum of $\binom{n}{n-2}$ integers [on hold]
Consider the following equation
$$
y^n=\sum_{k=1}^{\frac{n(n-1)}{2}} x_k,
$$
where $x,y,n,x_k\neq 0$ are integers.
Although I found a lot of material about how to express an integer as a sum of ...
5
votes
1answer
172 views
Functional equation for general number fields
When it comes to general number fields beyond $\mathbb{Q}$, the litterature is not so abundant in analytic number theory. For instance over $\mathbb{Q}$, for primitve Dirichlet characters modulo $q$, ...
3
votes
1answer
547 views
A new generalisation of dimension? part 2
I worked this theory : A new generalization of the dimension?
I have a theorem about dimensions which is more general and simple than for matroids.
Definition 1: A structure $S$, is a pair $(X, \...
1
vote
2answers
157 views
Reference request: Functions of bounded variation in one real variable
Is there a good reference for facts and theorems about BV real valued functions? I’m looking for something with much more than say Stein and Shakarchi 3, or Evans and Gariepy. Thanks!
1
vote
0answers
90 views
+50
Rate of convergence for difference between conditional and marginal probability
Suppose $X\sim \text{Bin}(2n,p)$ and $X_1,X_2\sim\text{Bin}(n,p)$ are independent, with $X_1+X_2=X$. I'm interested in the rate of convergence for the absolute difference
$$
\left\vert P(X>c|X_1\...
3
votes
1answer
232 views
Is it possible to define a linear $A_\infty$-category as a special kind of an $\infty$-category?
A functor $N\colon\mathrm{Cat}_{A_\infty}\longrightarrow\mathrm{Cat}_\infty$ is constructed in a paper [1] by Faonte. This gives a way to get an $\infty$-category by starting with an $A_\infty$-...
3
votes
0answers
41 views
Proof that superstable theories with no Vaughtian pairs have no imaginary Vaughtian pairs
In 'Elementary pairs of models' by Bouscaren, she mentions with a remark at the end that if $T$ is a superstable theory then $T$ has a Vaughtian pair if and only if $T^\text{eq}$ has a Vaughtian pair, ...
1
vote
0answers
26 views
Quasilinear elliptic problem on fractal domain
Consider the following quasilinear elliptic equation
$$\nabla_x (A(x,u(x),\nabla_x u(x))) + f(u,x) = 0 $$
on a bounded domain $\Omega$, augmented with homogeneous Dirichlet boundary data: $$u|_{\...
2
votes
1answer
59 views
Quasilinear elliptic problem: Ellipticity-type conditions
Consider the following quasilinear elliptic equation
$$\nabla_x (A(x,u(x),\nabla_x u(x))) + f(u,x) = 0 $$
on a bounded domain $\Omega$, augmented with homogeneous Dirichlet boundary data: $$u|_{\...
5
votes
0answers
122 views
Beilinson and Deligne's Motivic Polylogarithm and Zagier Conjecture
Where can I find the preprint Motivic Polylogarithm and Zagier Conjecture by Beilinson and Deligne? I see it referenced in a lot of papers but no one seems to host a copy.
6
votes
0answers
113 views
Is there a version of Weyl's law for graph Laplacians?
Is there a version of Weyl's law or a local Weyl's law for eigenvectors of the graph Laplacian?
For some context, a colleague in statistics has encountered eigenvectors of the Laplacian for certain ...
9
votes
3answers
503 views
Reference request for wild 3-manifolds
I’m looking for a text on 3-manifolds that focuses on wild/pathological objects, similar to Bing’s work in the field. I know basic algebraic topology (homotopy, homology, cohomology) and have read ...
16
votes
2answers
818 views
A multicategory is a … with one object?
We all know that
A monoidal category is a bicategory with one object.
How do we fill in the blank in the following sentence?
A multicategory is a ... with one object.
The answer is fairly ...
34
votes
2answers
2k views
Mathematical research in North Korea — reference request
Question: Where can one find information on which areas of mathematics
are represented at which of the more than 20 universities in the
Democratic People's Republic of Korea (DPRK), and on which ...
0
votes
0answers
19 views
Splittings for generic flows on a vector bundle
Question: Consider a smooth vector bundle $\pi:V\to B$ and the space $\mathcal{F}$ of $C^k$ linear flows $\Bbb{R}\times V \to V$ endowed with the strong $C^k$ Whitney topology. Is it true that for all ...
1
vote
0answers
25 views
Rotation rates for a linear flow on a vector bundle
The following linear ODE on $\Bbb{C}$
$\dot{z} = (a + i b)z$
has solutions $z(t) = e^{(a+ib)t} z(0)$. Hence the real part $a$ captures expansion rate and the imaginary part $b$ captures rotation ...
3
votes
0answers
44 views
How to show that a continuous family of symmetric matrices is uniformly positive?
My problem : I have a family of $4 \times 4$ symmetric matrices. More precisely consider an interger $d$, a real $\lambda> 0$ and define the family $S_{\lambda}$:
$ \{A(\lambda,x_1,x_2) ; (x_1,...
2
votes
0answers
28 views
Flat or linkless embeddings of graph with fixed projection
The problem of finding whether a given planar diagram of a graph, with over- and under-crossings, is a linkless embedding or not has unknown complexity (Kawarabayashi et al., 2010). My first question ...
2
votes
0answers
66 views
L-functions of tempered automorphic representations
Let $G$ be a reductive group over the adele ring $\mathbb A_F$ of a number field $F$. Let also $r$ be a complex finite dimensional representation of the $L$-group $r:{^LG}\to GL(V)$.
It is generally ...
5
votes
2answers
141 views
Enumeration of lattice paths of a specific type
One of the approaches to "Special" meanders led (in particular) to the following question:
What is the number $a_{m,n}(\ell)$ of $\ell$-step paths from $(1,1)$ to $(m,n)$ using the ...
6
votes
2answers
259 views
Outer Hodge groups of rationally connected fibrations
I believe the following is true and well known.
Theorem (?). Let $X$ and $Y$ be smooth, irreducible, projective varieties over $\mathbb{C}$. Let
$$
f\colon X\rightarrow Y
$$
be a surjective map with ...
2
votes
1answer
207 views
Thematic programs for collaborative research (similar to the one in Bonn) [closed]
The Hausdorff Institute in Bonn periodically organizes thematic junior trimester programs, which "give young mathematicians (postdocs, junior faculty) the opportunity to carry out collaborative ...
0
votes
0answers
41 views
Resolvent estimate of compact perturbation of self-adjoint operator
Let $T$ be a selfadjoint operator on Hilbert space $H$. Then we know that there is a resolvent estimation $$\left\lVert (\lambda-T)^{-1}\right\rVert = \frac{1}{dist(\lambda,\sigma(T))}, \ \lambda \in \...
0
votes
0answers
106 views
Final step in Coppersmith?
In the final step in Coppersmith technique we have $n$ polynomials (possibly non-homogeneous) in $\mathbb Z[x_1,\dots,x_m]$ where $m\leq n$ and using elimination theory we extract the common integer ...
0
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0answers
83 views
(Semi-)Riemannian geometry for working PDE analysts
What is a good reference on (semi-)Riemannian geometry written for PDE analysts (that is, with main focus on analytical problems and approaches)?
The closest thing I know to this, are two books by ...
4
votes
0answers
68 views
Examples of Yang-Baxter monoids
Then we say that an algebra $(X,f,g,\circ,1)$ is a Yang-Baxter monoid if it satisfies the following identities:
$(X,\circ,1)$ is a monoid,
$f(x,1)=1,f(1,x)=x,g(x,1)=x,g(1,x)=1$
$x\circ y=f(x,y)\circ ...
0
votes
1answer
82 views
Analytic approach to geodesic connectedness in Semi-Riemannian manifolds
Can you point out a reference (or references) that deal with analytical methods (rather than methods from differential geometry) for the study of geodesic connectedness on Semi-Riemannian manifolds?
3
votes
1answer
96 views
What “mild solution” means, and how to find it?
In this paper: Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem Byszewski studied this form of functional-differential nonlocal problem (1)...
5
votes
4answers
432 views
How to organize collaborations? Managing communication within the team [closed]
What is an effective tool for managing the communication within a small team of coauthors working on a paper (when face-to-face interaction is not possible)?
I've previously used back-and-forth email ...
0
votes
0answers
34 views
Anisotropic elliptic problems
Where can I find a reference on the following anisotropic problem?
$$(\bullet) \qquad \begin{align*} \nabla_x (A(x) \nabla_x u(x,y)) + \Delta_y(K(y) \ast u(x,y))\end{align*}=0, $$
where $(x,y) \in \...
0
votes
1answer
75 views
The definiton of a multiplier on a Banach algebra
Let $A$ be a Banach algebra. Some textbooks define a (left ) multiplier as a map $T:A\rightarrow A$ satisfying $T(ab)=T(a)b$ for all $a,b\in A$ and assume that $A$ needs to be a without order Banach ...
1
vote
1answer
58 views
Elliptic interface problem without conditions on the interface
Consider an open domain $U$ split in two non-overlapping subdomains: $U = U_1 \cup U_2$.
For a model case, consider a ball split in a smaller ball and an anulus.
Consider the following elliptic ...
25
votes
1answer
432 views
“Matchmaking website” for project-specific mathematical collaborations [closed]
It seems that even in the age of Internet, most mathematical collaborations are born (and pursued) off-line.
However, I wonder if there exists a "matchmaking website" for mathematical ...
6
votes
1answer
131 views
Anisotropic perimeter and regularity of anisotropic minimal surfaces
1. Introduction.
By-now classical results assert that minimal surfaces (in $\mathbb R^n$) are generically "smooth" out of a "small" set.
Question. What are the known regularity results for ...
