# All Questions

**0**

votes

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7 views

### Multiplicative domains and conditional expectations

Let $M$ be an injective von Neumann subalgebra of $B(H)$. For a completely positive map $\phi:B(H)\to B(H)$, let $Mult(\phi)$ denote be the multiplicative domain of $\phi$. For any conditional ...

**0**

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11 views

### Maximize combinatorial sum for boolean function

I am trying to maximize the function
$$ S(f)=\sum_{j=0}^{n-\frac{n-1}{t}}(-1)^j{n-\frac{n-1}{t}\choose{j}}\sum_{i=0}^{\frac{n-1}{t}}(-1)^{f(i-j)}(t-1)^i{\frac{n-1}{t}\choose{i}} $$
for a function ...

**-5**

votes

**0**answers

15 views

### solve for three unknowns. [on hold]

Apple cost 97 dollars. Orange cost 56 and lemon cost 3. The total amount spent is 16047 dollars and total fruits bought is 240 and each one is bought atleast one. Calculate how many of each have been ...

**0**

votes

**0**answers

27 views

### Rationally building bridges from Jacquet-Langlands to Langlands functoriality conjectures

For now I mainly worked on very classical proofs (viz. Bolte & Johansson, Bergeron) of the Jacquet-Langlands correspondence, but I hope to be able to understand in what this special case lead ...

**3**

votes

**0**answers

23 views

### The (global) theory of Borel equivalence relations

What do we know about the complexity of the theory of Borel equivalence relations, with the Borel reducibility order $\leq_B$?
That is, let $\mathcal{B}$ be the set of all Borel equivalence ...

**1**

vote

**0**answers

35 views

### If $G$ is compact, $H \leq G$ open, $V$ an irreducible $H$-rep, is $\text{Ind}_H^G$ semisimple?

Let $G$ be a compact group, $H$ a normal open subgroup, and $K$ a $p$-adic field (so that not all $G$-reps with coefficients in $K$ are semisimple). If $V$ is an irreducible $H$-representation with ...

**1**

vote

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16 views

### Graphs where each edge belongs to the same number of 1-factors

Let $G$ be a simple connected graph that has at least one 1-factor. We'll define:
$G$ has property A iff it is edge-transitive.
$G$ has property B iff each edge belongs to the same number of ...

**0**

votes

**1**answer

28 views

### Estimate maximal coefficient of a polynomial from a circle containing all roots

Suppose I have a polynomial
$$
p(x)=\sum_{i=0}^n p_ix^i.
$$
For simplicity furthermore assume $p_n=1$.
As it is well known we may use Gershgorin circles to give an upper bound for the absolute ...

**0**

votes

**0**answers

19 views

### On existence of right units with control of their norms

Does, there exist a Banach algebra with a family of right units with norms converging to 1, but without right unit of norm 1?

**-2**

votes

**1**answer

42 views

### Lack of parabolicity of PDE due to invariancy under diffeomorphisms?

Let a nonlinear differential equation is invariant under all diffeomorphisms, then we get lack of parabolicity?

**2**

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**0**answers

48 views

### Ergodic theory reference for converging sequences of matrices

I have been told that the following is a well known theorem in ergodic theory & have been given the book by Furstenberg as a reference. However, I cannot find such a statement in it. Would anyone ...

**4**

votes

**1**answer

94 views

### Is the Tate conjecture known for etale covers of products of curves

Let $X$ be a surface over a finitely generated field $k$. The Tate conjecture predicts that, for $l$ a prime number invertible in $k$, the Chern class map from Pic$(X) \otimes \mathbb Q_l$ to the ...

**-1**

votes

**0**answers

32 views

### Property of $\limsup$ in $\ell_1$ [on hold]

Let $w$ be any element in $\ell_1$, and $(w_n)$ be a bounded sequence in $\ell_1$ that converge to 0 pointwise. I want to prove
...

**1**

vote

**1**answer

94 views

### Lower bound for a prime gap occurring infinitely often

In his striking paper of may 2013, Zhang showed the existence of an even integer $g\lt 70,000,000$ such that $g$ is a prime gap occurring infinitely often. What is the best unconditional lower bound ...

**3**

votes

**1**answer

25 views

### In the definition of the Heegard Floer surgery exact triangle, what exactly is the correspondence between Whitney triangles and periodic domains?

I'm reading Osváth-Szabó's notes on Heegard Floer homology, in particular about the surgery exact triangle.
On page 14 (numbered 42 on the document), they describe an isomorphism between the space of ...

**5**

votes

**1**answer

243 views

### Tight prime bounds

This is a cross-post of this question on MSE. I would not usually do this, but have decided to in this case since it has had no responses having been posted as a bounty question. I did not delete the ...

**1**

vote

**0**answers

33 views

### Tensor product of commutators vs. commutator in a tensor product

Let $R$ be a (noetherian) commutative ring, and let $V$ and $W$ be finitely generated free $R$-modules. Let $X \subseteq \mathrm{End}_R(V)$ and $Y \subseteq \mathrm{End}_R(W)$ be finite subsets, and ...

**1**

vote

**1**answer

127 views

### Integer points on $y^2=x^2-x^3+x^4$

Does the Diophantine equation $y^2=x^2-x^3+x^4$ have solutions other than
$x=1,y=1$? Interestingly, the Diophantine equation $y^2=x^2-x^3+x^5$ has such solutions: $x=3,y=15$, $x=5,y=55$, ...

**9**

votes

**1**answer

197 views

### History of the connection between Riemann surfaces and complex algebraic curves

As noted in the question "Links between Riemann surfaces and algebraic geometry", there are strong connections between Riemann surfaces and algebraic geometry - for example, compact Riemann surfaces ...

**2**

votes

**0**answers

20 views

### Cusp points in Alexandrov spaces

Given a space of bounded integral curvature (by which I mean a topological surface with an intrinsic metric, such that the sum of excesses of any finite collection of non-overlapping simple triangles ...

**-1**

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**0**answers

66 views

### Long cycles in $\text{Sym}(n)$ [on hold]

Let $x,y \in \text{Sym}(n)$ (symmetric group on $\{ 1,2,\ldots,n \}$) and $z:=xy$.
Question: What non-trivial sufficient conditions (on $x$ and $y$) for $z$ to be a cycle of length $n$ do we know?
...

**2**

votes

**0**answers

26 views

### Looking for N-dimensional spheres in the configuration space of the colorful Tverberg problem

Here we use standard notation for Tverberg's theorem: Dimension $d$, number of partition blocks $r$, and $N=(r-1)(d+1)$.
The configuration space of Tverberg's theorem is the simplicial complex ...

**2**

votes

**1**answer

32 views

### Are lightface \Delta-1-1 classes of reals describable with hyperarthmetic formulae?

I'd appreciate if someone could check my reasoning. Suppose $S$ is a lightface $\Delta^1_1$ class of reals. I want to argue that there is a computable $\Delta^0_\alpha$ formula $\phi(Y)$, for ...

**-2**

votes

**0**answers

47 views

### Basis for the rational functions [on hold]

The rational functions $f(x)$ are given by $f(x) = \frac{P(x)}{Q(x)}$ where $P(x)$ and $Q(x)$ are polynomials. What bases for the rational functions are generally used in numerical analysis?

**0**

votes

**1**answer

39 views

### Topology : Study on Separation Properties [on hold]

I want an example of a completely regular space which is not a normal space. I have tried a lot but am unable to construct any example

**6**

votes

**0**answers

93 views

### Borel-Serre compactification of $\mathbb{H}^3 / SL_2(\mathcal{O}_K)$

Let $\mathbb{H}^3$ be the three-dimensional hyperbolic space. Let $K$ be an imaginary quadratic number field and $\mathcal{O}_K$ its ring of integers. Then $SL_2(\mathcal{O}_K)$ acts on $\mathbb{H}^3$ ...

**1**

vote

**0**answers

89 views

### Modular form, number of divisors [duplicate]

The Fourier expansion of Eisenstein series $E_k$ $(k \ge 4)$, which are modular forms, as well as the quasimodular $E_2$, involves powers-of-divisors $\sigma_{k-1}(n) = \sum_{d|n} d^{k-1}$.
Is there ...

**2**

votes

**3**answers

189 views

### Cardinality of $C^*([0,1])$ [on hold]

What is the cardinality of the continuous dual of $C([0,1])$ (the set of continuous functions from $[0,1]\to \mathbb{R}$)?

**-2**

votes

**0**answers

76 views

### k to 12 philippines [on hold]

i just want to ask this question, hope you will answer..what will happen to students who didn't undergo the senior high school in k to 12, students who graduated in the old curriculum in ched the not ...

**-1**

votes

**1**answer

39 views

### NonLinear Maps and homogeneity [on hold]

An example of a function $\phi : R^2 \to R$ such that $\phi(av) = a \phi(v)$ but $\phi$ is not linear.
So I know that I need to find a function that has linear homogeneity but doesn't have the ...

**2**

votes

**0**answers

55 views

### $G$-invariant part of products of determinants of minors

Let $G = SL_n$; then for any tuple $\lambda$ such that $\sum \lambda_i = n$, define $f_\lambda(g)$ as the product of the determinants of successive minors of lengths $\lambda_i$ of $g$ (e.g. for ...

**5**

votes

**0**answers

137 views

### Factors of the polynomial $X^n-a$

I am interested in the polynomial $X^n-a$ in $\mathbb{Q}[X]$, for some $a\in \mathbb{Q}^*$, and would like to know the irreducible factors of it. Is there something in the literature which gives a ...

**-3**

votes

**0**answers

66 views

### Is there a group-theoretic proof of the Riemann rearrangement theorem? [on hold]

The analytic proofs are easy to understand but they don't explain why commutativity breaks down when you go from finite sums to infinite sums of real numbers. I suspect that this involves the action ...

**1**

vote

**0**answers

24 views

### Generators for lattice polytopes

Let $V$ be a finite set of integral vectors in $\mathbb{R}_n$. Consider the real (positive) convex cone $\mathbb{R}^+V$ spanned by $V$. We can assume that all vectors in $V$ are extremal in ...

**8**

votes

**3**answers

574 views

### Not-lonely runners

The lonely runner conjecture
has several formulations.
They all involve a number $n$ runners running on a circular track,
each with a different speeds, and the conjecture is that each runner is ...

**1**

vote

**1**answer

29 views

### Compact imbedding - reference request

I am looking for reference to the following imbedding theorem
Theorem
For any $s>1/2$ fractional Sobolev space $W^{s}_2(0,1)$ imbeds compactly into $C([0,1])$.
I know how to prove it but I need ...

**-2**

votes

**0**answers

63 views

### How subset is a set is proved in ZF system? [on hold]

I guess that all subset is a set is guaranteed by the axiom of separation in ZF system. Otherwise the notion of power-set will not make sense.
But I wander how it's proved. I guess that the prove ...

**1**

vote

**0**answers

42 views

### Number of faces of a polytopal subdivision

Let $\mathcal{P}$ be a (bounded) polytope in $\mathbb{R}^d$ and let $\mathcal{C}$ be a polytopal subdivision of $\mathcal{P}$ [1].
Is there a known tight upper bound in the number of polytopes in ...

**8**

votes

**1**answer

593 views

### Removing an article from arxiv [on hold]

I put up my paper on arxiv before sending it for submission. But now the journal I wish to submit it to is not accepting it since its already been published (or because its publicly available). Is ...

**3**

votes

**0**answers

100 views

### The embeddings $S^{6} \to S^{7}$ and $S^{7}\to S^{8}$

Is the standard smooth structure of $S^{7}$ the only structure for which each of the following canonical embedding is an smooth embedding?:
1)$S^{6}\to S^{7}$
2)$S^{7}\to S^{8}$

**2**

votes

**0**answers

103 views

### Universal cover of elliptic curve without a point

This is something that I perhaps would be expected to know, but don't. Let $E_\tau$ be the elliptic curve ${\mathbb C}/({\mathbb Z +\mathbb Z} \tau)$. Consider the complement of a point in $E_\tau$,
...

**2**

votes

**0**answers

54 views

### Degree of join of two varieties

Let $X\subset\mathbb{P}^n$ be an irreducible variety of degree $d$ and dimension $n-4$. Let $L\subset X$ be a line of mulitplicity $m$ in $X$. Assume that $m+1\leq d$ so that the general line spanned ...

**5**

votes

**1**answer

225 views

### Serious introduction to the Langlands program for nonspecialist

I recently became interested in the Langlands program and hope to learn more.
For context, I am an analytic number theorist but have some light background in algebraic number theory and modular ...

**0**

votes

**0**answers

28 views

### Any software that can symmetrize input sets?

Is there any software that contains symmetrization techniques ex. polarization, Steiner Symmetrization etc. I suppose not.
Which software would you suggest for rigid transformations?
Thank you

**0**

votes

**0**answers

36 views

### Calculating the the ratio of two Dirac delta functions as the limit of the ratio of nasent delta functions?

I am in a situation where I find myself with the ratio of Dirac delta functions. Specifically, I find myself with the ratio of the nascent deltas:
$\frac{\lim_{\varepsilon \rightarrow ...

**5**

votes

**0**answers

90 views

### Hecke-module structure implicit in definition of automorphic forms in Borel-Jacquet's Corvallis article

Let $G$ be a connected reductive group over a number field $F$, $G_\infty=\prod_{v\mid\infty} G(F_v)$, $\mathbf{A}$ the adèles of $F$, $\mathbf{A}_f$ the finite adèles of $F$. Fix a maximal compact ...

**-2**

votes

**1**answer

63 views

### What does “group size” mean in the -G option of directg in nauty? [on hold]

To be sure I understand the definitions used in the nauty user manual: An automorphism group size (for a digraph) is the number of re-labelings (including the trivial original digraph) of the ...

**13**

votes

**0**answers

189 views

### function field analogy and global/absolute geometry

The "function field analogy" seems to be a topic that is considerably bigger than any one existing writeup conveys. There are several old question on MO and and MathSE that ask for details. One of the ...

**3**

votes

**0**answers

43 views

### Symplectic sum and Symplectic cut

The symplectic sum of Gompf and the symplectic cut of Lerman are known to be inverse of each other, in the sense that if you apply one of these first and the other one afterward, you obtain the ...

**0**

votes

**0**answers

22 views

### mixed semi definite and second order programming complexity order

Consider the following mixed semi definite and second order programming:
$\begin{array}{l}
\mathop {{\rm{min}}}\limits_{\bf{X}} \,{\rm{Tr}}\left( {{\bf{XA}}} \right)\\
{\rm{s}}{\rm{.t:}}\, & ...