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

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4
votes
1answer
110 views

Reference for an unbiased definition of a symmetric monoidal category

In the references I know, a symmetric monoidal category is defined as a monoidal category equipped with some additional data, so in particular the monoidal product is a functor $$ \mathcal{C}\times ...
4
votes
0answers
34 views

Sobolev-Poincaré inequality for curl-integrable functions

Let $B=B(r)$ denote a ball of radius $r$ in $\Omega \subset \mathbb R^d$ and $$ u_B := \frac1{|B|}\int_B u \, dx. $$ The standard Sobolev-Poincaré inequality states that if $u \in W^{1,p}(\Omega)$, ...
1
vote
0answers
23 views

Symmetry conjecture for minimal dilatation pseudo Anosov mapping classes

The conjecture is something like the following: The minimal dilatation among pseudo-Anosov mapping classes on a surface $S_{g,n}$ is realized by $\rho\circ\omega$ where $\omega$ is supported on a ...
2
votes
1answer
65 views

References about spectral theory on Hyperbolic space

Can anyone suggest me some books or papers that include details about spectral theory on Hyperbolic spaces or related topics such as scattering theory on Hyperbolic spaces? After some googling, I ...
7
votes
1answer
210 views

Reference request, zeta function is rational function via Riemann-Roch?

I am looking for a reference to a proof that the zeta function of a function field in one variable over a finite field $\mathbb{F}_q$ is a rational function in $q^{-s}$ by using the Riemann-Roch ...
1
vote
0answers
34 views

Multivariable polynomial interpolation via evaluations from entrywise powers of a point

I am interested in multivariate polynomial interpolation. Within computational complexity theory, I use it to create efficient reductions between counting problems. In the univariate case, there is ...
2
votes
0answers
55 views

Generalized Hurwitz Spaces

In this question all the varieties are over $\mathbb{C}$. Classic Hurwitz spaces $\mathcal{H}_{g,r}$ are moduli spaces of simple branched coverings $f \colon X \to \mathbb{P}^1$ of degree $d$, where ...
14
votes
1answer
325 views

Are symplectic methods used in (classical) Economics?

The tl;dr question is this: are economists using coordinate-free formulations in studying theory? Borrowing from classical mechanics, the framework I have in mind for classical economics--involving ...
3
votes
0answers
123 views

Where can I find a proof of this result on optimal tessellation of a unit square?

Here is an excerpt from the paper "The Hexagon Theorem" by Donald J.Newman Does anyone know where I can find a proof of the underlined statement? Newman states it without a proof, and I could get ...
1
vote
1answer
89 views

Suggestions for dealing with the “timed” balls-into-bins model

Definitions: Let $T$ (for "time") be a random variable $T \sim \text{Exp}(\lambda)$ and $\Delta t$ is a realization (or called an observed value) of $T$. Let $D$ (for "delay") be a random variable $D ...
4
votes
0answers
78 views

$H^s$ norm of a solution of a nonlinear Schrödinger equation

I'm reading the paper "Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on $\mathbb{R}^3$ by Colliander, Keel, Staffilani, Takaoka and Tao. They study the ...
1
vote
0answers
29 views

Perturbation of a Fredholm sections which preserves compactness of 0-set

I am learning Morse-Bott-Floer theory and found the following cool paper http://de.arxiv.org/abs/1310.5080 by P. Albers and D Hein. In order to prove a cup-length estimate on the number of critical ...
5
votes
1answer
104 views

Example of a $G$-sphere that is not a $G$-representation sphere

Let $G$ be a finite group with the discrete topology. To set terminology: a $G$-sphere is a sphere equipped with a continuous $G$-action a $G$-representation sphere is a $G$-sphere obtained from an ...
4
votes
1answer
90 views

Loss of derivative of subelliptic operator

Consider the differential operator $P$ on $\mathbb{R}^2$, given by $P = \frac{\partial^2}{\partial x^2} + x^2\frac{\partial^2}{\partial y^2}$. Clearly it is elliptic everywhere except on the $y$-axis. ...
6
votes
3answers
643 views

Catalan numbers as sums of squares of numbers in the rows of the Catalan triangle - is there a combinatorial explanation?

This question arose from an answer to my recent question How many traces are there on Temperley-Lieb, Fuss-Catalan, Iwahori-Hecke, Birman-Wenzl-Murakami-Kauffman, ... algebras? What I need from that ...
2
votes
2answers
238 views

Is Eilenberg-Maclane $\wedge$ Moore space the spectrum of the cohomology theory $H^*(\ ,G)$?

In the web page http://www.encyclopediaofmath.org/index.php/Moore_space it can be found the following statement: If $K(\mathbb Z,n)$ is the Eilenberg–MacLane space of the group of integers ...
1
vote
1answer
48 views

Limiting absorption principle

I would like to know if there is a book (or a paper) which can give me an introduction to LAP. I tried to read some papers by myself, but I don't feel comfortable. I think that I need the basic ideas ...
3
votes
0answers
246 views

What's the name of this branched covering?

I've come across a double cover of $\mathbb P_1(\mathbb C)$, ramified at $[1:1]$ and $[-1:1]$ in homogeneous coordinates, given as the quotient by the natural $\mathbb Z/2\mathbb Z$-action generated ...
15
votes
1answer
383 views

How many traces are there on Temperley-Lieb, Fuss-Catalan, Iwahori-Hecke, Birman-Wenzl-Murakami-Kauffman, … algebras?

There is a theorem (I believe by Ocneanu) that the Markov trace on the tower of Temperley-Lieb algebras is (essentially) unique. What about just traces on separate algebras? That is, take one of ...
1
vote
1answer
91 views

If $q^k n^2$ is an odd perfect number with Euler prime $q$, are the following statements known to hold in general? [on hold]

(Note: This has been cross-posted to MSE. However, I feel that it is more likely to receive a good answer here, because I believe that it is a research-level question. For the mathematicians who ...
3
votes
0answers
63 views

Reference for a lemma on the asymptotic upper density of special sets with large gaps and intervals

Update. Based on Anthony Quas' comment below, the proof can be made sensibly shorter and the lemma can be slightly generalized by weakening the old assumption (iii). In a joint paper that I am ...
7
votes
0answers
71 views

Equation of the curve corresponding to a polarization of an abelian surface

Let $\mathbb{C}^2/\Lambda$ be a polarized abelian surface. I think it is well-known how to write down the equation of the divisor corresponding to the polarization, in terms of theta functions etc. ...
6
votes
2answers
145 views

Pseudodifferential operators on spaces with boundary

Consider the upper half space $\mathbb{R}^n_{+} = \{x = (x_1,..,x_n) \in \mathbb{R}^n : x_n \geq 0\}$. Consider the Laplacian on this space with either the Dirichlet boundary condition or the Neumann ...
3
votes
1answer
115 views

Enriques classification of algebraic surfaces in characteristic zero

I am searching for a reference about the classification of algebraic surfaces over an arbitrary algebraically closed field of characteristic zero. In the 1949 book "le superficie algebriche" by ...
0
votes
0answers
28 views

Automorphisms of a differential field and transcendence degree

Let $(\mathcal{F},+,\times,\partial)$ be a differential field, and let's define its automorphism group $Aut(\mathcal{F})$ as the group, under composition, consisting of all bijective maps ...
2
votes
1answer
241 views

Earliest source for a Lie algebra construction

I am looking for the earliest reference to the fact that any associative algebra becomes a Lie algebra with bracket $AXB-BXA$, where $X$ is a fixed element of the algebra. This is observed in the ...
1
vote
1answer
126 views

Level-Lowering in Weight 2

Let $N$ and $p$ be relatively prime integers with $p$ a prime. Suppose $f$ is a weight $k=2$ (normalized, cuspidal, etc) newform of level $\Gamma_1(N) \cap \Gamma_0(p)$. I seem to recall the existence ...
-5
votes
0answers
173 views

Are there “adelic” L-functions? [closed]

Following Tom163's answer to this question, I would like to know whether L-functions defined through adelic representations (as defined in https://projecteuclid.org/euclid.em/1317758108) have been ...
3
votes
2answers
162 views

$\mathcal S'(\mathbb R^d)$ is separable [closed]

I Think the statement is true, but I struggle to find a reference for the fact that the space of tempered distributions equipped with the weak-* topology is separable. Thank you for your help!
-2
votes
1answer
68 views

How does deletion-contraction affect chromatic number? Can it increase chromatic number? [closed]

Question: In graph theory, contracting an edge or deleting an edge are basic operations in many topics such as graph minors or Wagner's theorem on planar graphs. And I'm interested in how these ...
0
votes
0answers
30 views

Reference request for some “irregularities of distribution” papers

I would like to ask if anyone has access to any of the following papers: 1. J. G. van der Corput, Proc. Kon. Ned. Alcad. v. Wetensch., Amsterdam, 38, 813-821 (1935). 2. J. G. van der Corput, ibid. 38, ...
3
votes
2answers
156 views

Examples of toric threefolds

I am looking for examples of smooth projective toric threefolds $\mathbb P_\Delta$ such that the rational polytope $\Delta$ has only pentagonal faces and hexagonal faces. I quickly searched for ...
5
votes
1answer
176 views

Higher-dimensional category theory on objects

I would like to know if there exists a satisfying generalization of higher-dimensional category theory on objects, that doesn't forget the inner structure of objects. Usually, what people do is to ...
3
votes
0answers
138 views

Correspondence between real forms and real structures on complex Lie groups

I asked this in MSE, but without success, so I hope, it will be suitable here. E.B.Vinberg and A.L.Onishchik in their book give the following two definitions. For a complex Lie group $G$ its real ...
0
votes
0answers
35 views

interpolation between Bochner spaces

Is there a reference for the interpolation result stating the existence of an embedding \begin{equation} L^2(I;W^{2,p}(\Omega)) \cap H^1(I;L^p(\Omega)) \hookrightarrow ...
6
votes
2answers
190 views

What methods do we have to understand the spectrum of matrices with restricted entries?

Consider questions of the form (or the "most probable value of" version of these questions rather than the "largest possible"), What is the largest possible spectral radius of a $n \times n$ matrix ...
4
votes
0answers
80 views

On various “extension closures” and “orthogonals” in triangulated categories

A vague form of my question is the following one: for a class of objects $D$ of a triangulated category $C$ we consider the class $E$ of objects that satisfy $Mor_{C}(d,e)=\{0\}\ \forall d\in D$; ...
2
votes
0answers
42 views

Multiplication operators are sectorial [migrated]

Consider the multiplication operator $M_a$ on $L^p(M)$, where $M$ is a Riemannian manifold, and $a$ is a non-negative function. An operator $A$ is said to be sectorial if there exists $\theta \in (0, ...
3
votes
1answer
132 views

Preprint by Wall on Sjogren's theorem

In their account http://dx.doi.org/10.1016/0022-4049(87)90048-X of Sjogren's theorem, Cliff and Hartley refer to two articles: [9] B. Hartley, A note on a lemma of Sjogren relating to. dimension ...
3
votes
0answers
94 views

n-homology of a Harish-Chandra module

Let $G$ be a connected real reductive Lie group and let $K$ be its maximal compact subgroup. Let $P=MAN$ a parabolic subgroup. Let $K_M^0=M^0\cap K$ be connected component of the maximal compact ...
2
votes
0answers
65 views

Resolvent estimate of hyperbolic Laplacian [closed]

Consider the Laplacian $-\Delta$ on the hyperbolic space $\mathbb{H}^n$. For $\lambda \in \mathbb{C} \setminus [0, \infty)$, do we have resolvent estimates of the form $$\Vert (-\Delta - \lambda ...
4
votes
3answers
185 views

Enumerating cosets of the modular group

Suppose we chose the generators $f(z) = z+1, g(z) = z-1, h(z) = -1/z$ for the modular group $\Gamma$ (i.e. the group of fractional linear tranformations $z \mapsto (az +b)/(cz+d)$ with $a,b,c,d \in ...
2
votes
0answers
163 views

References for 'Theory of $p$-adic Galois Representations by Fontaine & Ouyang'

Presently I am reading the 'Theory of $p$-adic Galois Representations by Fontaine & Ouyang'. I am finding it difficult for eg. the initial sections on $l$-adic geometric representation of finite ...
3
votes
1answer
171 views

Model structure on non-negative differential graded algebras with homological grading

I was wondering if there exists a model structure on the category of non-negative differential graded algebras with homological grading. To be more precise: Let $Ch_{k}$ the model category of ...
3
votes
0answers
78 views

Localized at $p$ integral representations of finite elementary $p$-groups

Let $C_p$ be a cyclic group of prime order $p$. Let $F=C_p^n=C_p\times\dots\times C_p$ ($n$ times). I would like to to classify finite dimensional representations of $F$ over ${\mathbb{Z}}$. However, ...
0
votes
1answer
68 views

Reference for measures of commutativity needed

I'm looking for an appropriate measure to quantify the extent to which two matrices commute. In other words, if A and B are two n×n Hermitian matrices, and [A,B]=C. I'd like a function μ:Cn×n→[0,∞) ...
8
votes
0answers
125 views

Complete list of exceptions and efficient algorithm for Waring's problem

2 weeks ago, Samir Siksek http://arxiv.org/abs/1505.00647 proved more than 150-years-old conjecture that every positive integer other than 15, 22, 23, 50, 114, 167, 175, 186, 212, 231, 238, 239, 303, ...
0
votes
0answers
49 views

Global existence solutions NLS

Let's consider the following NLS in $\mathbb{R}^3$ $$i\partial_t\psi=-\Delta\psi+\vert\psi\vert^2\psi$$ How to prove that $H^2$-solutions are globally in time? Can someone suggest references to me?
3
votes
0answers
62 views

Integrability of Continuous Tangent Subbundles

Are there any field of mathematics, except dynamical systems, where one needs to integrate continuous sub-bundles of the tangent space? More specifically given a smooth manifold of $M$ and a ...
4
votes
2answers
180 views

hyperbolic structure on Figure–8 knot complement

I was trying to understand the proof of the fact that there is a hyperbolic structure on Figure–8 knot complement initially from Thurston's notes and then from some online notes; but unfortunately I ...