# All Questions

**0**

votes

**0**answers

67 views

### asymptotic behavior of minimum dilatations on punctured surfaces

Let $l_{g,n}$ be the logarithm of minimum dilatation for pseudo-Anosov homeomorphisms on surface of genus $g$ with $n$ punctures. Let $n$ be fixed and $g$ varies. Is the asymptotic behavior of ...

**3**

votes

**3**answers

211 views

### reference for list of left-regular representations of real associative algebras

Suppose $\mathcal{A}$ is a unital associative algebra over $\mathbb{R}$. If we identify $\mathcal{A} = \mathbb{R}^n$ then the $\mathcal{A}$ multiplication corresponds to particular linear maps on ...

**7**

votes

**3**answers

1k views

### Monad arising from operad

It's known that from every operad arises a cartesian monad whose algebras are the algebras for the operad. Leinster proved that there are different operads from which arise the same monad, in this way ...

**0**

votes

**0**answers

11 views

### Conditioned sum of n Poissons versus unconditioned Poissons

Let $\theta >1$ and take independent random variables $Z_k \sim \text{Poisson}(\theta/k)$ for $1 \leq k \leq n$ and let $Z_k^*$ have marginals like the $Z_k$ conditioned on $\sum_1^n k Z_k = n$:
...

**0**

votes

**0**answers

21 views

### a solution of nonlinear wave equation

I am looking for a solution for the following wave equation:
$u_{xx}+u_{yy}=F(x,y)u_{tt}$
where
$F(x,y)=\sqrt{E(x,y)/P(x,y)}$
and $E(x,y)$, $P(x,y)$ are linear functions.
Is there any analytic ...

**-5**

votes

**0**answers

33 views

### Mathematics example that didn't quite undestand [on hold]

Find all value k such that the function x^3-3x+k has one real solution ? Thanks

**1**

vote

**0**answers

56 views

### Applications of the Weak and Weak$^*$ topologies to PDEs?

Chapter $3$ of Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis constructs and explains the Weak and Weak$^*$ topologies over a Banach Space $E$.
The most ...

**2**

votes

**2**answers

615 views

### Delauney triangulation in high (>20) dimensions

Hi all,
I know that its very hard to find the Delauney triangulation of high dimensional spaces, especially if there are several thousand points that need to be triangulated.
So I was wondering . . ...

**13**

votes

**5**answers

2k views

### Matrix representation for $F_4$

Has anyone ever bothered to write down the 26-dimensional fundamental representation of $F_4$? I wouldn't mind looking at it. Is it in $\mathfrak{so}(26)$?
I'm familiar with the construction of the ...

**75**

votes

**16**answers

19k views

### What if Current Foundations of Mathematics are Inconsistent? [closed]

The title of the question is also the title of a talk by Vladimir Voevodsky, available here.
Had this kind of opinion been expressed before?
EDIT. Thanks to all answerers, commentators, voters, ...

**14**

votes

**1**answer

498 views

### Operator norms of circulant matrices

The definition and basic properties of circulant matrices can be found here: http://en.wikipedia.org/wiki/Circulant_matrix.
For complex numbers $a_1,\ldots,a_n$, I will use the notation
$$
...

**9**

votes

**2**answers

2k views

### roots of sum of two polynomials

I believe that there is no common theory for finding roots of polynomial sum. In my case I have
$$P_{n}(x)+AQ_{n}(x)$$.
I am wondering how roots of this sum depend on $A$?

**9**

votes

**1**answer

766 views

### Wrong-way Frobenius reciprocity for finite groups representations

This is a typical lazy mathematician question, so do not hesitate to close it and recommend me to do my homeworks...
Let $H$ be a subgroup of a finite group $G$, and let $Res_H^G$ and $Ind_H^G$ the ...

**9**

votes

**3**answers

697 views

### Can a metric conformal to a Kahler metric be Kahler?

Let $X$ be a non-compact complex manifold of dimension at least 2 equipped with a Kahler metric $\omega$. Take a smooth positive function $f : X \to \mathbb R$, and define a new hermitian metric on ...

**155**

votes

**27**answers

19k views

### What are some reasonable-sounding statements that are independent of ZFC?

Every now and then, somebody will tell me about a question. When I start thinking about it, they say, "actually, it's undecidable in ZFC."
For example, suppose A is an abelian group such that every ...

**3**

votes

**0**answers

231 views

### Restriction of a global moduli functor that admits a coarse moduli space

Let $F:(Sch/k)^{o}\to Sets$ be a functor, where $Sch/k$ is the category of schemes over a field $k$. Suppose that $F$ admits a coarse moduli space, let it be $M$. Consider a $k$-point $x\in M$ (which ...

**6**

votes

**1**answer

114 views

### Algebraic cobordism (of a point) outside the geometric diagonal

This question is about the state of current knowledge regarding Voevodsky's algebraic cobordism of a point $\mathrm{MGL}^{*,*}(\mathrm{Spec}\,k)$. That the geometric diagonal ...

**12**

votes

**5**answers

491 views

### Applications of space filling curves

I am seeking articles where a space filling curve has been used as a theoretical application, such as in the study of general orthogonal polynomials.

**6**

votes

**1**answer

320 views

### Is it true that irreducible generic representations of $G_2(F)$ are self-dual?

Let $G_2$ be the split exceptional group of type $G_2$ and $F$ be a p-adic field. Is it true that every irreducible smooth representation of $G_2(F)$ is self-contragredient? If the answer is Yes, can ...

**9**

votes

**0**answers

129 views

### Simplest example of failure of finite Galois descent in algebraic $K$-theory?

Let $E \to F$ be a $G$-Galois extension of fields.
What is the simplest example where the natural map $K(E) \to K(F)^{hG}$ is not an equivalence on connective covers (i.e., where finite Galois ...

**7**

votes

**0**answers

70 views

### Are the unwound thin realization and fat realization homotopy equivalent?

This is a question about a theorem (proposition 2) in the article--On the homotopy type of classifying spaces
Recall some definitions first:
Given a category $\mathcal{C}$ internal in ...

**6**

votes

**1**answer

235 views

### Is polynomial convexity a topological invariant?

Is the property of being polynomially convex a topological invariant?
In other words, assume that $M$ and $N$ are two compact subset of $n$-dimensional complex Euclidean space which are homeomorphic. ...

**11**

votes

**1**answer

406 views

### Elements of arbitrary large order in the first Galois cohomology of an elliptic curve

Let $E$ be an elliptic curve over $k=\mathbb{Q}$. Consider $H^1(k,E)$.
In this answer Daniel Loughran writes: "I'm pretty sure that this cohomology group has elements of arbitrarily large order". I ...

**274**

votes

**15**answers

38k views

### Why do roots of polynomials tend to have absolute value close to 1?

While playing around with Mathematica I noticed that most polynomials with real coefficients seem to have most complex zeroes very near the unit circle. For instance, if we plot all the roots of a ...

**16**

votes

**2**answers

827 views

### Probability of two vectors lying in the same orthant

Let $S^{d-1} = \{x \in \mathbb R^d: \|x\| = 1\}$ denote the unit sphere in $\mathbb R^d$. Let $v$, $w$ be drawn uniformly at random from $S^{d-1}$, conditioned on their inner product being equal to ...

**6**

votes

**0**answers

216 views

### A non-hyperfinite type III factor from an action of the free group on the circle

We define below a von Neumann algebra $\mathcal{M}$ from an action of the free group on the circle, and we prove that $\mathcal{M}$ is a non-hyperfinite type III factor.
Question : Is ...

**3**

votes

**1**answer

2k views

### The Paley-Wiener theorem and exponential decay.

Consider a function whose Fourier transform is supported on a half-ray:
$$
A(t)=\int_0^\infty \omega(E) e^{-iEt}d E,
$$
where I can suppose $\omega(E)\geq 0$ and any suitable regularity conditions on ...

**5**

votes

**1**answer

510 views

### Books about Capacity theory

While I was studying the book Variation et Optimisation de formes by Antoine Henrot and Michel Pierre, I encountered a section about the capacity associated to the $H^1$ norm, which is defined for ...

**3**

votes

**1**answer

428 views

### About Theorem 3.2 in 'introduction to spectral theory of automorphic forms' by Iwaniec

In Theorem 3.2 of 'Introduction to spectral theory of automorphic forms' by Iwaniec,the first bound is about the coefficients of automorphic forms
$$\sum_{|n|\le ...

**2**

votes

**1**answer

148 views

### Fundamental Units in Totally Real Cubic Fields

How much is known about the fundamental units in totally real cubic fields? For example, Daniel Shanks has a family of totally real cubic fields for which the fundamental units are known; those with ...

**19**

votes

**3**answers

1k views

### A generalization of the triangle counting problem for simple weighted graphs

One nice identity is that $$\operatorname{tr}(A^3)/6$$ counts the number of triangles of a graph with adjacency matrix $A$. It also implies that triangle counting in a graph can be performed in ...

**14**

votes

**4**answers

2k views

### What is a section?

This question comes out of the answers to Ho Chung Siu's question about vector bundles. Based on my reading, it seems that the definition of the term "section" went through several phases of ...

**13**

votes

**2**answers

3k views

### Separable and algebraic closures?

I have no intuition for field theory, so here goes. I know what the algebraic and separable closures of a field are, but I have no feeling of how different (or same!) they could be.
So, what are the ...

**1**

vote

**1**answer

209 views

### derivative of Riemann zeta function

One can of course give a power series for the derivative of RiemannZeta. But is there a "closed form", e.g. expressible in the field of functions generated by Zeta and Gamma and some constants?

**7**

votes

**1**answer

650 views

### Iterated forcing and CH

I need some help with this theorem: if $P_\beta=\langle P_\alpha,\dot{Q}_\alpha:\alpha\leq\beta\rangle$, $\beta<\omega_2$, is a CSI of proper forcings, $P_\alpha\Vdash \lvert ...

**1**

vote

**2**answers

353 views

### Models of the natural numbers in ultrapowers in the universe.

Our question arises from wondering about the systems of natural numbers in models ZFC + Con(ZFC) and ZFC + $\neg$Con(ZFC). In thinking of the systems of natural numbers of these models, we came to ...

**7**

votes

**4**answers

439 views

### Picard groups of quartic K3 surfaces

Does anyone know where I can find examples of quartic K3 surfaces for which the Picard group is known? I'm really interested in examples where there are explicit constructions of the divisors ...

**10**

votes

**2**answers

1k views

### Hilbert transforms of measures

Given a finite measure $\mu$ on the real line $\mathbb R$, one definition of its Hilbert transform is $(H\mu)(y) =\frac{1}{\pi}(PV)\int \frac{d\mu(x)}{x-y}$ which is known to exist almost everywhere ...

**10**

votes

**4**answers

2k views

### Which topics/problems could you show to a bright first year mathematics student?

I am teaching a one semester course (January to June) to first year students pursuing various different degrees. Because there are students studying actuarial science, physics, other sciences, other ...

**0**

votes

**0**answers

113 views

### asymptotics of primes in arithmetic progressions

If $a$ and $q$ are given coprime positive integers, what is the best known error term for
$$
\sum_{p<x,\,p\,\text{is prime},\,p\equiv a \pmod q} \frac{\log p}p-\frac{\log x}{\varphi(q)}?
$$
Is it, ...

**5**

votes

**1**answer

676 views

### Wanted: differential coming from higher genus surface in Heegaard Floer Homology

I am interested in studying moduli of complex surfaces which arise in computing the differential on the Heegaard Floer Homology chain complex. In particular, I am interested in the generic case, when ...

**15**

votes

**17**answers

15k views

### Undergraduate Differential Geometry Texts

Can anyone suggest any basic undergraduate differential geometry texts on the same level as Manfredo do Carmo's Differential Geometry of Curves and Surfaces other than that particular one?
(I know a ...

**36**

votes

**25**answers

7k views

### Where can square roots come from when they are not distances?

In a recent survey "Supergeometry in Mathematics and Physics", Kapranov points out cases in which observable quantities of immediate interest are represented as bilinear combinations of more ...

**6**

votes

**3**answers

538 views

### functions with same area

I have two real valued functions $f_1$ and $f_2$ such that
$\int_0^Tf_1=\int_0^Tf_2=a_1$
$\int_0^Tf_1^2=\int_0^Tf_2^2=a_2$
$\forall \\ t, f_1(t),f_2(t)\in[0,1]$
Now,I want to construct a family ...

**0**

votes

**1**answer

113 views

### spectrum of an induced algebra

Let $G$ be a reductive group defined over an algebraically closed field $k$ and $B$ be a fixed Borel subgroup of $G$. Suppose $X=Spec(R)$ is an affine scheme with $B$ rationally acting on it; hence ...

**48**

votes

**17**answers

11k views

### Parodies of abstruse mathematical writing

Perhaps under the influence of a recent question
on perverse sheaves,
in conjunction with the impending $\pi$-day (3/14/15 at 9:26:53),
I recalled a long-ago parody of abstruse mathematical language
...

**8**

votes

**2**answers

721 views

### Does the category of topological symmetric spectra satisfy the monoid axiom ?

In the paper "Symmetric spectra"by Hovey, Smith and Shipley, they say that they don't know if the monoid axiom holds for topological symmetric spectra. This paper was written in 1998 so I am wondering ...

**8**

votes

**4**answers

905 views

### Notation for eventually less than

Is there some existing notation for
\[f(n)\leq g(n)\] for sufficiently large n
Apart from just writing that itself?
I'm thinking of something compact like the ...

**1**

vote

**1**answer

532 views

### the existence of compact Kahler manifolds satisfying some Hodge numbers' restrictions

Given any $n\geq 2$, is there an example of $n$-dimensional compact Kahler manifold such that its Hodge numbers satisfy $h^{1,1} = h^{2,2} < h^{3,3} = h^{4,4} < h^{5,5} = h^{6,6} < \cdots ...

**0**

votes

**0**answers

48 views

### a two dimensional integer bijection

I want to try to find a specific two-dimensional linear integer bijection. This is to be used in a double sum rearrangement. It's kind of complicated, but I would really appreciate if anybody has any ...