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

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Contraction semigroup

Let $(X, \mu)$ be a finite measure space and let $A$ be a non-negative self-adjoint operator which generates a contraction semigroup $e^{tA}$ on $L^2(X, \mu)$. If additionally, we have that $e^{tA}$ ...
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1answer
87 views

Fourier coefficients of real analytic functions on an n-dimension torus

Let $(\mathbf{R}^n,\langle\;,\; \rangle)$ be the n-dimensional euclidean space endowed with the standard inner product. For a lattice $L\subseteq \mathbf{R}^n$ we let $cov(L)$ denote the covolume of ...
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43 views

When is a $2$-Calabi–Yau triangulated category the cluster category of a QP?

Keller–Reiten's main theorem in Acyclic Calabi–Yau categories implies that if $\mathcal{C}$ is a $2$-Calabi–Yau (algebraic) triangulated category admitting a cluster-tilting object $T$ such that the ...
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1answer
67 views

Renorming into contraction

In Pazy's book on semigroups he mentions (page 18) that when you have a commuting family of operators $B(t)$, such that $$ \sup \| B(t_1) .. B(t_n) \| \le M $$ for all finite choices $t_1, .. t_n$ ...
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0answers
65 views

Arithmetic quotients of Bruhat-Tits buildings for groups over local fields of positive characteristic

I have been led to believe that there is a result giving a description of the quotient of a Bruhat-Tits building $\Delta(G,k)$, for a semisimple algebraic group $G$ over a non-archimedean local field ...
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1answer
217 views

Reference for a lemma on étale maps

The Stacks Project has the following really nice Lemma concerning étale maps of rings: Let $A\rightarrow B$ be a finitely presented, étale morphism of rings. Then there exists a presentation $$ ...
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1answer
136 views

Is $K^0(X)\to K_0(X)$ monomorphic for a noetherian scheme $X$?

This question is related to the MO questions What is the difference between Grothendieck groups K_0(X) vs K^0(X) on schemes? and Does a fully faithful functor between triangulated categories induce ...
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1answer
156 views

Does a fully faithful functor between triangulated categories induce embedding of their Grothendieck groups?

Let $\mathcal{A}$, $\mathcal{B}$ be two triangulated categories and $F: \mathcal{A}\to \mathcal{B}$ be a triangulated functor between them. Then $F$ induces an homomorphism between their Grothendieck ...
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1answer
136 views

Spectrum of the Laplacian on p-forms on the sphere

In this paper the authors give an explicit description of the eigenforms and spectrum of the Laplacian acting on $p$-forms on the round sphere $S^n$, apparently citing an unpublished computation of ...
2
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1answer
66 views

Generators of the colored braid group (two colors), reference

I consider the group $B_{n,n}$, the braids, colored in two colors, say all odd strings are black and all even strings are white. It is easy to find a set of generators for $B_{n,n}$: $$ \begin{cases} ...
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0answers
88 views

Reference to parabola lemma

I am looking for a previous reference to the following very simple geometric lemma, which I use in my paper [arXiv:1503.03462]: Let $P$ be the parabola $y=x^2$. Let $a,b,c,d$ be four points on $P$ ...
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0answers
42 views

Strongly minimal set with DMP

Recall that a strongly minimal theory $T$ has the Definable Multiplicity Property (DMP) if for all natural $k$, $m$ and $\varphi(\bar{x},\bar{b})$ of rank $k$, multiplicity $m$, there exists a formula ...
11
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1answer
187 views

Fair cake-cutting between groups

The cake-cutting game is usually played between individuals. What if we try to play it between groups? A certain land has to be divided between two states. ‎There are $n$ citizens in each state. ...
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4answers
413 views

Rate of convergence in the Law of Large Numbers

I'm working on a problem where I need information on the size of $E_n=|S_n-n\mu|$, where $S_n=X_1+\ldots+X_n$ is a sum of i.i.d. random variables and $\mu=\mathbb EX_1$. For this to make sense, the ...
3
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0answers
125 views

Moser estimates?

Consider $u$, an $L^2$ solution to the uniformly elliptic equation $(\partial_t^2 + L)u = 0$ on a ball $B_1$ of radius 1 centered at $(t_0, x_0)$, say, where $t$ can be treated as a "time" variable. I ...
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0answers
67 views

Motivation for the existence of periodic solutions [on hold]

I have been reading the book Critical Point Theory and Hamiltonian System by Mawhin and Willem, as well as several other papers on the existence of periodic solutions for equations of the form ...
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0answers
95 views

Simply connected Kahler manifold without any effective divisor

Does anyone know an example of a simply-connected compact Kahler manifold without an effective divisor? Does anyone know a reference on this topic? Thanks!
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2answers
113 views

Sum of two unbounded self-adjoint operators

Let $A$ and $B$ be two unbounded self-adjoint operators. From this mathoverflow post, for instance, we know that $A + B$ is self-adjoint on $\mathcal{D}(A) \cap \mathcal{D}(B)$ if $A$ and $B$ are ...
4
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1answer
174 views

Young tableau with no i in row i, name that derangement

This question has its genesis in a group assignment: $k$ students are to be given oral exams. Each student will be asked one distinct question from $n$ questions given to them earlier, no two students ...
13
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1answer
393 views

When complex conjugation lies in the center of a Galois group

Let $K \subseteq \mathbb{C}$ be a number field (I'm fixing an embedding), and assume $K/\mathbb{Q}$ is Galois with Galois group $G$. Let $\tau \in G$ denote complex conjugation. This question ...
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0answers
62 views

About some distributive laws in the Bousfield lattice

It is know that for any $\alpha$-well generated tensor triangulated category $\mathcal{T}$ the collection of Bousfield classes forms a set, furthermore this set is a complete lattice, denoted by ...
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0answers
74 views

Size of the eigenfunction of Laplacian (reference request)

It is a classical Sobolev inequality that if $\phi$ is an eigenfunction of the Laplace-Beltrami operator on a $n$-dim compact Riemannian manifold $M$ with eigenvalue $\lambda$ then ...
1
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1answer
88 views

A $C^{*}$ algebra associated to a graded $C^{*}$ algebra

A $C^{*}$ algebra $A$ is graded by $\mathbb{Z}_{n}$ iff it can be acted by $\mathbb{Z}_{n}$. So we associate the $C^{*}$ algebra $A\rtimes \mathbb{Z}_{n}$ to a $\mathbb{Z}_{n}$-graded $C^{*}$ ...
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2answers
584 views

Is every positive integer a sum of at most 4 distinct quarter-squares?

There appears to be no mention in OEIS: Quarter-squares, A002620. Can someone give a proof or reference? Examples: quarter-squares: ${0,1,2,4,6,9,12,16,20,25,30,36,...}$ 2-term sums: ${2+1, 4+1, ...
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2answers
57 views

Reference request : Besov spaces on ubounded domains

As I am relatively new to these matters, I would like to know if you could provide me a reference for Besov spaces on unbounded domains, because when I checked the first tome of Triebel's Theory of ...
5
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0answers
110 views

Universal anti-Horn classes?

Is there published work about universal anti-Horn classes? (See also related question Is there any research of universal algebras axiomatized by non-Horn clauses? asking about universal classes ...
4
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1answer
130 views

On one class of Somos-like sequences

This question is motivated by integrability of the sequence mistakenly arisen in the question Does this sequence always give an integer? Let $m_1,\ldots, m_{k-1}$ be positive integers and sequence ...
4
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1answer
110 views

Diffusion semigroup generated by Laplacian

Let $M$ be a complete Riemannian manifold and $\Delta$ denote the Laplacian on it. Also assume that the spectrum of $-\Delta$ lies inside $[a, \infty)$. Let $P_t, t > 0$ denote the diffusion ...
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0answers
37 views

Reference for using an algebra of meromorphic functions to extend a Lie algebra

For example, let $\mathfrak{g}=\mathfrak{sl}_{2}\left(\mathbb{C}\right)$, let $s_{0}=1$, $s_{1}=-1$, $s_{2}$=0, $s_{3}=\infty$ in $\mathbb{P}_{1}\left(\mathbb{C}\right)$ and $\mathcal{R}$ is the ...
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0answers
67 views

Domain of $A^{1/2}$ on $L^2(\mathbb{T}^2)$

Let $A$ be a densely defined unbounded self-adjoint operator defined on $L^2(\mathbb{T}^2)$, where $\mathbb{T}^2$ stands for the 2-torus. It is known that $A$ is positive, that is, $\langle Au, ...
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1answer
59 views

4D Duoprisms based on nonconvex polygons

A duoprism is a polytope that can be expressed as the Cartesian product of two polytopes (each of dimension $\ge 2$). Four-dimensional duoprisms in particular have been studied: $$P \times Q = \{ ...
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1answer
75 views

methods for situations where well-posedness criteria hold but global solutions do not exist

I have been learning PDEs (more specifically, nonlinear dispersive equations (Schrödinger/wave/ Klein-Gordan equations etc...)) through the harmonic analysis methods. And I have read a couple of ...
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1answer
891 views

Has this strong number theoretic conjecture of Euler been proved, and where could I find such a proof?

Polya cites this work of Euler as an example of a conjecture which Euler considered impossible to doubt, and yet still needing a demonstration. It is on pages 90-98 of "Induction and Analogy in ...
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1answer
86 views

Tunnel number of Pretzel knots

I would like to know the tunnel number of $n$-pretzel knots. I have searched and found nothing for any $n>3$. When $n=2$, $t(K)=1$ or $2$ depending on the number of twists, which is proved in a ...
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1answer
187 views

What's the minimum amount of knowledge to start doing research? [closed]

There are cases in which you have too much knowledge of something to do anything interesting ,and cases in which a lack of experience with a problem (and the prejudices about it) helps someone solve ...
3
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1answer
95 views

Reference of $\hbar$-differential operator from symplectic geometry perspective

I am reading Bates and Weinstein's book 'Lectures on the Geometry of Quantization'. In Chapter 6, they defined the $\hbar$-differential operator, and showed (Theorem 6.7) that the Lagrangian ...
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2answers
528 views

How do I apply the Boolean Prime Ideal Theorem?

I have become aware of an amazing phenomenon from a myriad of questions and answers here on MathOverflow: many of the results that I would typically prove using the Axiom of Choice can actually be ...
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0answers
63 views

Characterization of locally conformally flat manifolds: strange application of Frobenius theorem

(Crossposted from math.SE because of the lack of replies) In Hamilton's Ricci Flow (by Chow, Lu, Ni, pp. 29-31, see here) they show that a Riemannian manifold $(M^n,g)$ is locally conformally flat ...
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5answers
826 views

Deep Learning / Deep neural nets for mathematician

I am interested in finding out the math ideas behind the technologies that are under the umbrella of "Deep Learning" or "Deep neural nets". Most of the papers/books that are often quoted in ...
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0answers
174 views

Seeking reference to result in this talk by Voevodsky [duplicate]

In this presentation by Vladimir Voevodsky [1], he mentions a result that there is a formula over the natural numbers with a single free variable such that one can prove that there is no algorithmic ...
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0answers
90 views

Derived categories of modules categories

Does anyone know if there is a note or a paper about the derived category of the category $\sigma[M]$ where $M$ is a left module over a ring?, and some uses of this.
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69 views

Fixed Points of the Friedman Stanley Jump

Consider the situation of a pair $(X,E)$, where $X$ is a standard Borel space and $E$ is an invariant equivalence relation on $X$*. The Friedman-Stanley jump of this pair is an equivalence relation ...
5
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1answer
147 views

Reference Request: Grouplike Algebras over the little $n$-cubes operad are $n$-fold loop spaces

In Geometry of the iterated loop space, Peter May proved his famous recognition theorem, which is, in a simple form, stated on page 3 as the following. There exist $\Sigma$-free operads ...
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89 views

Estimates of entropy of functional spaces

Let $M^n$ be a compact $n$-dimensional manifold. For $k\geq 0$ let us denote by $C^k(M)$ the Banach space of $k$ times continuously differentiable functions, and $B_{C^k}$ denote the unit ball of it. ...
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1answer
197 views

What happens to continuous spectrum upon discretization?

Excuse me for a bit of an vague question, but I haven't been able to find a definite answer for this for quite some time. My question is regarding (mostly non-normal )linear operators and their ...
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0answers
28 views

Help with an inequality in Cazenave's book “Semilinear Schrodinger equations” [migrated]

I'm reading Cazenave's book "Semilinear Schrodinger equations" and I found this inequality at page 84 $$\vert\vert u_1\vert^\alpha u_1-\vert u_2\vert^\alpha u_2\vert\vert\leq C (\vert ...
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1answer
200 views

Reference request for division algebras, over $\mathbb{Q}_{p}((t))$

I was looking for a possible reference that would answer the following question, Let $\mathbb{Q}_{p}$ be the $p$-adic numbers and $\mathbb{Q}_{p}((t))$ be the field of Laurent polynomials over ...
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0answers
87 views

How does one compute a colimit of monoidal categories?

The question is in the title. I'm also happy to get answers about (your favorite adjective) monoidal categories. Here's a guess: In order to compute a colimit of monoids we can push everything down ...
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0answers
54 views

Name for condition on map of cancellative monoids

Let $M,N$ be cancellative monoids with identity $\epsilon$ and suppose that $k\colon M\rightarrow N$ is a function such that $k(\epsilon)=\epsilon$ for all $a,b\in M$, there exists $v\in N$ such ...
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203 views

category theoretic approach to Sylow theorems and finite group theory?

Is there a category theoretic approach to Sylow theorems? More generally, is there an exposition of finite group theory in terms of category theory which would include Sylow theorems and little facts ...