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

**1**

vote

**0**answers

35 views

### Reference request for $R$-index

Let $R$ be a noetherian domain with field of fractions $F$, let $V$ be a finite-dimensional $F$-vector space, and let $M,N \subseteq V$ be $R$-lattices in $V$ (finitely generated $R$-submodules of $V$ ...

**5**

votes

**1**answer

146 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

**0**answers

28 views

### Differential of the adjoint quotient map

My question is regarding a paper by R.W Richardson titled "Derivatives of invariant polynomials on a semisimple Lie Algebra" ** . In this paper, he reports on computations of the rank of the ...

**4**

votes

**1**answer

154 views

### Open questions on (finite) tensor categories

I would like to know about problems on (finite) tensor categories. I have read Etingof´s notes from his course at MIT. I have a question:
There exists any reference where I can find an open problem ...

**7**

votes

**4**answers

327 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 ...

**0**

votes

**1**answer

89 views

### separable BV space for PDE's, Whats stopping us? [on hold]

Consider the metric space BV(0,1) with the following metric
$$ d(u,v) = \|u-v\|_{L^1} + |TV(u)-TV(v)| $$. It is separable, compact, uniformly bounded and complete. So What is the really obvious thing ...

**3**

votes

**1**answer

214 views

### Reference request - Jacquet module and asymptotic of matrix coefficients

Hello,
I would like to know some nice references about the relation between asymptotics of matrix coefficients of representations of reductive groups over local fields, and the pairing between the ...

**10**

votes

**0**answers

277 views

### Goodwillie's notes from MSRI Lecture Series

Does anyone know where I can find an electronic version of Goodwillie's (unpublished) notes from the MSRI Lecture Series in Spring, 1990? They're mentioned/cited as such in work of Dundas-McCarthy, ...

**-2**

votes

**0**answers

86 views

### direct proof for existence of antiderivative [on hold]

I wonder if anybody has tried the following kind of direct proof for the existence of an antiderivative of an analytic function on a star-shaped domain.
Theorem: Let $f:D \to \mathbb{C}$ be an ...

**0**

votes

**1**answer

279 views

### Equidimensionality of stalks of $\operatorname{Proj} S$ when $S$ is equidimensional.

I would like to know a reference of the following statement (or counter example).
Let $S$ be a (commutative) Noetherian standard graded ring over a local ring, i.e., $S = S_0[S_1]$, where $S_0$ is ...

**2**

votes

**0**answers

155 views

### Is Carlos Simpson's Descent available online?

I am not sure whether this question is suitable for MO. Is the paper "Descent" by Carlos Simpson in the book "Alexandre Grothendieck: A Mathematical Portrait" page 83-142 (or a similar version of that ...

**10**

votes

**1**answer

898 views

### Connes's unpublished manuscript on correspondences, anyone?

There exist unpublished notes on correspondences of von Neumann algebras due to Connes. This is often cited, but I've never seen a copy. It would be nice to have this, say, to maybe look further into ...

**2**

votes

**0**answers

43 views

### Geometric unfolding of a difference equation

Does anyone know a link to the (superb) slides of a talk given by Zeeman in 1996, I think (with same title as this question)? It used to be at www.math.utsa.edu/ecz/gu.html .

**5**

votes

**3**answers

381 views

### Where was it first stated that there are no 4-transitive finite groups other than symmetric, alternating and Mathieu groups?

It seems to be well-known that the six-transitive finite groups are the symmetric and alternating groups, and the only other four-transitive finite groups are the Mathieu groups (the statement can be ...

**7**

votes

**1**answer

196 views

### Do semialgebraic sets depend outer semicontinuously on their defining polynomials?

Consider a compact (semialgebraic) ball $B\subset \mathbb{R}^n$ and a semialgebraic set $A=A(f_1,\cdots,f_s)\subset \mathbb{R}^n$ defined through some representation in terms of polynomials ...

**1**

vote

**0**answers

106 views

### Homeomorphism of fibers of holomorphic maps

EDIT (after the comment by Jason Starr): Let $X$ be a complex algebraic (or, more generally, analytic) variety, possibly singular and non-compact. Let $f\colon X\to D^*$ be a proper algebraic morphism ...

**7**

votes

**0**answers

191 views

### Finding non convex functions satisfying a weak form of convexity, without the axiom of choice

If a real-valued function $f$ over reals satisfies $$ (1) \; \; \; f({x+y\over2})\le {f(x)+f(y)\over2}, $$and it is continuous, then it is not hard to see that $f$ is indeed convex. On the other ...

**2**

votes

**0**answers

16 views

### Fractional parts of two multiples [duplicate]

There is a theorem (I can't remember its name) saying that for any irrational number $x$ and any $0<a<b<1$, there exists a positive integer $n$ such that $\{nx\}\in (a,b)$, where $\{\cdot\}$ ...

**3**

votes

**0**answers

53 views

### Some questions about the Lévy monoid of certain densities

Let $\bf H$ be a set, $f: \mathcal P({\bf H}) \rightharpoonup \bf R$ a partial function, and $\mathcal{D}$ the domain of $f$.
Next, denote by $\mathcal M(f)$ the set of all (total) functions $\theta: ...

**5**

votes

**0**answers

48 views

### Chromatic numbers for coloring-constrained graphs

I am interested in any and all articles about chromatic numbers applying to constrained colorings of a graph. For example, if a graph must be (properly) colored so that there is a 2-color path ...

**4**

votes

**1**answer

277 views

### Is the Kolmogorov complexity of at least one string of a given length equal to its length? [on hold]

Is it true that for all strings of a given length (for any alphabet with more than one symbol), at least one has a Kolmogorov complexity equal to its length?
If the answer is Yes, is there a proof of ...

**11**

votes

**1**answer

2k views

### Gluing Markov processes

I am looking for a reference on the gluing together of strong Markov processes to get a new one.
Here is an example of what I have in mind. Let $B^1, B^2, \ldots $ be independent one-dimensional ...

**1**

vote

**0**answers

60 views

### Category of equicontinuous sets of mappings

Does this category have a name? Does it have any literature?
Objects are topological vector spaces. A morphism from A to B is any equicontinuous set of linear mappings from A to B.

**11**

votes

**1**answer

304 views

### Examples and Counterexamples in Commutative Algebra

There are Counterexamples in Analysis and Counterexamples in Topology. Is there any similar book for commutative algebra? I want to see some more (counter)examples for Atiyah and MacDonald's book. Let ...

**0**

votes

**1**answer

159 views

### When is $a^{2^n}+1$ prime finitely often unconditionally?

Define generalized Fermat numbers following OEIS and mathworld.
For natural $a,n$ and $a$ even, the generalized Fermat number (GFN) is
$F_n(a)=a^{2^n}+1$.
Very large GFN primes are known (in the ...

**3**

votes

**1**answer

264 views

### Hypothesis test beyond simple hypotheses (mathematical statistics)

In mathematical statistics, the following problem (simple hypothesis test) is considered: given a data sample, test the hypothesis $H_0$ stating that all sampled values are values of a random variable ...

**5**

votes

**1**answer

169 views

### Definition of a normed ring

A normed ring "should" be a monoid object in the monoidal category of normed abelian groups. There are (at least) two choices of morphisms of normed groups, namely bounded or short homomorphisms, ...

**7**

votes

**1**answer

617 views

### Strong Markov property for Poisson point process

The question is thoroughly contained in the title. I just say that I would only like to find a reference for this question. I have searched in some books, to no avail.
Here is what I mean exactly. ...

**2**

votes

**0**answers

82 views

### Short exact sequences for amalgamated free products and HNN Extensions

I asked this question on math stackexchange (see here) but didn't get any answer so I thought I would post it here too:
If $A$ and $B$ are groups we have the following short exact sequence:
$$ 0 \to ...

**1**

vote

**0**answers

28 views

### Colorful Neighborhoods

Given:
$G:=\{V= \{v_1,\ ...\ v_n\},E\subset V\times V\}, n<\infty$, a symmetric complete, simple graph
$w:=\ \ E \ni e_{ij}\mapsto \mathbb{R}^+$, a weight function for the edges of $G$
$K:=\{c_1,\ ...

**10**

votes

**3**answers

568 views

### Distance between two knots

Are there some well-studied functions defining natural distance measures between two knots? One can imagine a function that counts, say, the minimum number of
moves, each of which passes one strand of ...

**0**

votes

**0**answers

29 views

### Reference request: Linear evolution equations of “hyperbolic type”

Does anyone have any accessable link to the following paper by Kato?
Linear evolution equations of “hyperbolic type”
Note: It is the first paper, not the sequel numbered by II. After several ...

**5**

votes

**2**answers

245 views

### A result of Sierpiński on non-atomic measures

There is a classical result commonly attributed to W. Sierpiński that reads as follows:
Theorem 1. If $f: \Sigma \to \bf R$ is a non-atomic (*) measure on a set $S$, then for every $X \in \Sigma$ ...

**15**

votes

**3**answers

1k views

### Good reference for studying operads?

Can you, please, recommend a good text about algebraic operads?
I know the main one, namely, Loday-Vallette "Algebraic operads". But it is very big and there is no way you can read it fast. Also ...

**3**

votes

**1**answer

179 views

### Minimal Birthdays

In combinatorial game theory: The birthday of a game is defined recursively as 1 plus the maximal birthday of its options, with the zero game having birthday 0.
Suppose we define the quasi-birthday ...

**6**

votes

**2**answers

303 views

### Is this almost-cosimplicial object familiar?

I have a sequence $X_0,X_1,\ldots$ of Abelian groups, along with face maps $d_0,\ldots, d_n: X_{n-1}\to X_n$ which satisfy the standard cosimplicial identities EXCEPT at the very bottom, where in ...

**2**

votes

**0**answers

150 views

### Was “arithmetical translation” (coding in the Goedel sense) ever a part of Hilbert's Program?

Was "arithmetical translation" (that is, coding in the Goedel sense) ever a part of Hilbert's Program? I ask this question for several reasons:
i) it gives the numerals |, ||, |||,.... an ersatz ...

**-1**

votes

**0**answers

38 views

### Alternative Geometries [migrated]

In our world, the distance between two points (in 2d) is defined as $\sqrt{(\Delta x)^2 + (\Delta y)^2}$. Suppose that in an alternative geometry, it was defined as $\sqrt[p]{|\Delta x|^p + |\Delta ...

**2**

votes

**3**answers

433 views

### The number of submodules of $\mathbb{Z}_q^n$

Observe $\mathbb{Z}_q^n = \mathbb{Z}_q \times \cdots \times\mathbb{Z}_q$ as a module over $\mathbb{Z}_q\equiv\mathbb{Z}/q\mathbb{Z}$, for general $q$.
I am interested in the following questions:
How ...

**0**

votes

**1**answer

60 views

### expressing in terms of sum of (double) schubert polynomial

It is well known that Schubert polynomials form a basis for the polynomial ring $\mathbb{Z}[x_1,x_2,x_3,...]$.
I am interested in knowing how to express a particular polynomial into sum of Schubert ...

**0**

votes

**1**answer

40 views

### Compact embedding and fractional Sobolev spaces in unbounded domain

It is known that there exists a compactness results involving fractional sobolev spaces in bounded domain. What about unbounded domain? More precisely, Under which conditions, we can extend the ...

**1**

vote

**1**answer

77 views

### How to prove the Hölder continuity of a function $u$ by evaluating $\int_{B_{\rho}(x_0)}\frac{|Du(x)|^{2}}{|x-x_0|^{n-2}} dx$?

I'm looking at a video on thin obstacle problem given by Arshak Petrosyan.
In his lecture, he uses the following results:
Let $0<\alpha<1$, and $B_1$ be the unit ball centered at origin in ...

**3**

votes

**0**answers

75 views

### Reference on the classification of (low rank) Gorenstein rings over $\mathbb{C}$

I am interested in the question of the classification of (low rank) Gorenstein rings over $\mathbb{C}$. The socle of a local algebra is the annihilator of its maximal ideal. A commutative local ring ...

**27**

votes

**6**answers

5k views

### Mathematician trying to learn string theory

I'm a mathematician. I want to be able to read recent ArXiv postings on high energy physics theory (String theory) (and perhaps be able to do research). I want to understand compactifications, ...

**0**

votes

**0**answers

186 views

### Quantities associated to deformed sheaves

I am trying to figure out what happens to "quantities" associated to a sheaf when one deforms it. I am actually interested in deforming a bounded complex of coherent sheaves but I want to make the ...

**4**

votes

**1**answer

135 views

### Questions about the regularity of the “norm” associated to a convex set

Suppose $K\subset \mathbb{R} ^n$ is a closed convex set whose interior contains the origin. We can assign a gauge function to $K$ as $g_{K}(x):=\inf\{\lambda>0 \mid x\in\lambda K\}$. $g_K$ has all ...

**8**

votes

**0**answers

158 views

### An abstract zero-sum problem

I would like to know whether the problem described below has appeared in the literature and/or whether similar questions have been studied. I would be very happy to find some references or, if none ...

**1**

vote

**0**answers

55 views

### Chain Rule for Maximal Correlation

Let a pair of random variables $(X,Y)$ be defined over finite alphabet $\mathcal{X}\times \mathcal{Y}$ with joint distribution $P_{XY}$. The maximal correlation $\rho(X;Y)$ between $X$ and $Y$ is ...

**3**

votes

**1**answer

109 views

### A clarification regarding analytic perturbation of metrics and Laplacian

This question is in reference to the following Mathoverflow question and the accepted answer to it. It seems to me that it is taken for granted that if the metric $g_t$ perturbs real analytically in ...

**1**

vote

**0**answers

93 views

### Expository papers for Feit–Thompson Theorem [duplicate]

Feit–Thompson theorem states that every finite group of odd order is solvable.
Its proof is near 300 pages so it is definitely not an easy paper to read without a prior knowledge about the general ...