# All Questions

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### Specific cases of the tangle hypothesis in terms of “classical” n-categories

As is well known, the tangle hypothesis of Baez and Dolan proposes that, for suitable definitions, the $n$-category of framed $n$-tangles in $n+k$ dimensions is the free $k$-tuply monoidal ...
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### Choosing Matrix Decomposition for Analysis

Consider a complex square matrix $A\in\mathcal{C}^{n\times n}$. Now let us discuss two kinds of the factorization of $A$, say, eigendecomposition and Schur decomposition because both of them are often ...
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### When is the image of a 2-dim l-adic representation associated to a modular form open

I know the following theorems by Serre: 1, The 2-dim l-adic representation associated to a non-CM elliptic curve is open. 2, The 2-dim l-adic representation associated the weight-12 cusp form ...
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### What is the chromatic number of the “conic hypergraph” on a non-singular plane cubic?

Can we color the points of a complex non-singular plane cubic curve with finitely many colors so that no conic intersects the curve at 6 points of the same color? If so, what is the smallest number ...
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### Construction of homogeneous Siegel domain from j-algebra

I am reading bounded homogeneous domain from Piatetski-Shapiro's book Automorphic functions and the geometry of classical domains'' and have questions on how to construct homogeneous Siegel domain ...
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### General extension of scalars and tensor products

My goal is to in a sense, create an additional set of "scalars" from the field of complex numbers, and the ring of integers. That will also maintain the property of being bilinear under bilinear forms ...
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### Can there be computable non-standard models of PA in a weaker sense?

By Tennenbaum's theorem, in the usual sense of computability for models, neither addition nor multiplication can be computable in a non-standard model of PA. Weak version: Can addition or ...
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### optimal bound in diophantine representation question

Given that, with integers $t \geq 1$ and $q \geq 3,$ there are solutions to $$x^2 - q x y + y^2 = - t q$$ with integers $x,y \geq 1,$ I was able to show that $$q \leq 1 + \frac{324}{25} t^2.$$ ...
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### Invertibility of a Cauchy-type matrix

I am trying to show with general (structural) arguments, that the following matrix \begin{align*} \begin{pmatrix} \frac{1}{3} & -\frac{1}{5} & -\frac{1}{7} & \frac{1}{9} \\ ...
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### On the separability of operator range

Let $T$ be an operator from a Banach space $X$ into a Banach space $Y$ and $1\leq p<\infty$. If $ST$ is compact for any operator $S$ from $Y$ into $l_{p}$, Is $T(X)$ separable? Or under what ...
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### log convexity for the norm of vector-valued function

Log convexity of various functions defined on the space of Hermitian matrices plays an important role in matrix analysis and probability theory. Given $v \in \mathbb{C}^n$, $D$ a diagonal matrix with ...
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### Growth of dimension of fixed spaces in $GL_n(\mathbb{Q}_p)$-representations

Let $\pi$ be a generic irreducible admissible representation of $GL_n(L)$, where $L$ is a $p$-adic field, $R$ is its ring of integers, and $\mathfrak{p}$ is its prime ideal. The conductor of $\pi$ ...
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### A completeness criterion for $\infty$-categories

We all know that for ordinary categories $\mathscr{C}, \mathscr{D}$ (with $\mathscr{C}$ small) the limit of a functor $F:\mathscr{C} \to \mathscr{D}$, if it exists, can be constructed by using ...
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### Equivalence between Diffie Hellman and Discrete Log

For which non-trivial groups, do we know that the Diffie Hellman problem and the Discrete Log are equivalent? Is there any group for which we suspect them to be different? Could there be a finite ...
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29 views

### Maximize mutual information

Assume $P \in \mathbb{R}^{n \times n}$ describe the joint distribution of the random variable $J$ over the finite set $\mathcal{X}\times \mathcal{X}$. I am interested in finding a right stochastic ...
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### Sitefel-Whitney class of bundles induced by a covering map

Let $S^m$ be the unit $m$-sphere. Let $P$ be a $m$-dimensional polyhedron with $k$-vertices, such that all the vertices of $P$ lie in $S^m$. The isometry group of $S^m$ is $Iso(S^m)=O(m+1)$. Let ...
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### Questions concerning convergence rate of Iterated Projections

Assume for simplicity $C_1,C_2,...,C_n\subset \mathbb{R}^m$ to be closed and convex subsets with $\underset{i=1}{\overset{n}{\bigcap{}}}C_i\neq\emptyset$. Let $x^0\in\mathbb{R}^n$ and define the ...
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### “Pythagoras number” for integral matrices

It is classically known that every positive integer is a sum of at most four squares of integers, i.e. every sum of squares of integers is a sum of four squares of integers. Now consider a symmetric ...
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### Critical with respect to chromatic, but not Hadwiger number

For any simple, undirected graph $G=(V,E)$ where $V$ is finite, we define the Hadwiger number $\eta(G)$ to be the maximum $n$ such that $K_n$ is a minor of $G$. Is there a graph $G$ on such that ...
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### Where does the name $NE(X)$ come from?

Why do we call the cone of curves(effective one cycles) on a variety $X$ as $NE(X)$, what does $NE$ stand for?
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### Generalization for Leray Hirsch theorem for Principal $G$-bundle

This is a general question: Is there a generalized Leray Hirsch theorem for Principal $G$-bundle? with $G$ finite group with discrete topology. I know it does not make sense to compare with original ...
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### Outline of Generic Seperable Banach Spaces don't have a Schauder Basis

So, I know P. Enflo showed that there is a separable Banach Space that doesn't satisfy the approximation property. My professor mentioned during class that in fact generic separable Banach Spaces ...
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### Representation theory of groupoids

Is there for a groupoid an representation theorem as Representation theorem of Wagner-Preston for inverse semigroups?
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### When are simple foliations strictly simple?

Any submersion $f: M → N$ defines a foliation of M whose leaves are the connected components of the fibres of $f$. Foliations associated to the submersions are called simple foliations. The foliations ...
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### On Holonomy in (regular) Riemannian Foliations

Right now, I am trying to understanding the role of holonomy fields on Riemannian foliations, which lead me to the following (probably topological) groupoid: Let $\mathcal{F}\subset M$ be a ...

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