# All Questions

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### What would you do with a new model of linear logic?

I have been working for some time with collaborators developing some models of linear logic which we are confident are new. However, none of us is deep enough in the field to answer the sceptic's ...
61 views

### $a \cos(x) + ib \sin(x)$ reduced to $\cos(x+iy)$form [closed]

As the titled suggests, is there is formula remotely near this expression? $a \cos(x) + ib \sin(x)$ reduced to $\cos(x+iy)$. Contextual basis, I'm required to convert a Laurent polynomial to a trig ...
53 views

### Optimality condition for strongly convex function under sparsity constraint

Let $f: \mathbb{R}^p \to \mathbb{R}$ be a $2s$-sparse strongly smooth, $2s$-sparse strongly convex and twice differentiable function. In other words, there exists positive constants $\alpha, L >0$ ...
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1 vote
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### Representing geodesic compactifications of $S^1\times \Bbb R$ as analytic sections over base (analytic) foliations

Given a smooth nested set of "partial" foliations $\mathcal F_{\alpha}=\big\lbrace e^{\frac{\alpha}{\log x}}: \alpha \in (1/k,k), x\in(0,1),k\in [1,\infty) \big\rbrace$ of $X^2=(0,1)^2$ with ...
1 vote
94 views

### Problem in understanding maximum principle for subharmonic functions

I am reading subharmonic functions and their properties from the book From Holomorphic Functions to Complex Manifolds by Grauert and Fritzsche. Let me first define what a subharmonic function is. ...
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73 views

### Classification of principally polarized abelian surfaces - reference request

I found in Encyclopedia of math https://encyclopediaofmath.org/wiki/Abelian_surface there is a claim that: "A principally polarized Abelian surface $(A,λ)$ is either the Jacobi variety $J(H)$ of ...
• 143
27 views

### Regular maps on hyperbolic plane for large number of vertices

I want to generate large regular maps of a tiling on hyperbolic space. How I can start doing that?
112 views

### Noether's formula for real algebraic surfaces

Is there a version of Noether's formula for the Euler characteristic of a surface for Real algebraic surfaces? Specifically, given $X$ a real algebraic compact smooth surface, what is the relationship ...
158 views

### What should be unipotent de Rham homotopy group?

What exactly should unipotent $\pi_1^\text{dR}$ be conceptually? What formal properties should it satisfy? This seems to be answered by Chen's theorem, which is stated in Corollary 3.269 of Multiple ...
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### Composition of Frobenius $n$-homomorphisms, characteristic-free?

This question is, as so often, a crossbreed of curiosity and laziness. The former has led me to an interesting, but somewhat unsatisfactory paper by Khudaverdian and Voronov (arXiv:2002.02395v2) and, ...
49 views

### Reference request: Fréchet embedding

Given a separable metric space $(X,d)$, we have an isometric embedding $X\to\ell^\infty$ given by taking $x_n$ the countable dense subset and sending $x\mapsto\lvert(x,x_n)-d(x,x_0)\rvert$. This ...
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1 vote
43 views

### Reverse mathematics on lightface $\Pi^1_1$-uniformization for unary relation

It is known that the following form of $\Pi^1_1$-uniformization is equivalent to $\Pi^1_1$-Comprehension over $\mathsf{ATR}_0$ (cf. VI.2.6 of Simpson's book) : (Kondo's uniformization theorem) For ...
• 2,754
149 views

### Estimating ${\left(\sum_{i=j}^k {x_i}\right)^2} \times \left\lvert\sum_{i=j}^k {a_i}\right\rvert$

Given two sets; $X = \{x_i : x_i \geq 0; i \in [\sqrt{n}]\}$ and $A = \{a_i : |a_i| \leq 1; i \in [\sqrt{n}]\}$ of size $n^{\frac{1}{2}}$ each, with the following properties \label{...
• 23
41 views

### Perron-Frobenius theory for operators on matrices

Let $A$ be a Hermitian linear operator on the space of $n\times n$ complex matrices. Let's suppose $A$ is "non-negative" in the sense that it preserves the cone of non-negative definite (...
• 53
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### Simple curves on hyperbolic tori

In the paper "Simple curves on hyperbolic tori" by McShane and Rivin, they show that if $T$ is a hyperbolic once punctured torus, one can define a norm on the homology $H_1(T,\mathbb{Z})$ by ...
• 7,061
96 views

### Extending a map between $A$ and $B$ to a map between $L(A)$ and $L(B)$

Are any known results about extending a map $\phi:A\to B$ to a map $\overline{\phi}:L(A)\to L(B)$ or $\phi':HOD(A)\to HOD(B)$? This seems like something that would have been investigated already, and ...
• 97
1 vote
66 views

### Unique polarization on a very general curve with Mumford-Tate

I try to understand why a very general curve (smooth, projective over $\mathbb{C}$) has an unique polarization up to scalar on the $H^1(X,\mathbb{Q})$. I was advised to look at the maximality of the ...
120 views

### Are there any interesting classes of limits containing finite limits?

Let $\Phi$ be a class of limit diagrams that contains all finite diagrams. Some examples include the classes $\Phi_{\kappa}$ of all diagrams of size bounded by a cardinal $\kappa$... but are there any ...
46 views

### Calculate the rotational volume that arises when the area enclosed by the curve 𝑦 = 𝑒^−𝑥^2 and the x-axis can rotate around the y-axis? [closed]

so my question for thiscalculus homework is : Calculate the rotational volume that arises when the area enclosed by the curve 𝑦 = 𝑒^−𝑥^2 and the x-axis can rotate around the y-axis? now am i ...
1 vote
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1 vote
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• 9,090
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### Degeneracy maps of Drinfeld modular curves

Over number fields, we have two natural degeneracy maps $$X_0(N)\leftarrow X_0(pN) \rightarrow X_0(N)$$ between the (compactified) moduli space of elliptic curves with level $pN$ and $N$ respectively (...
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### Are there outer models $V \subset W$ of $L$ such that $V$ is "far" from $L$ but $W$ is "not too far" from $V$?

In the following, whenever I say "$V_1$ is an outer model of $V_2$", I mean $V_1, V_2$ are transitive models of $\mathsf{ZFC}$, $V_2 \subset V_1$,and $ORD^{V_1} = ORD^{V_2}$. I am curious ...
• 1,193
1 vote
39 views

### Defining properties of categories out of an indicial category

$\newcommand{\Hom}{\operatorname{Hom}}$Suppose we want to define the category of arrows of $S$. Below are two forms of doing it. Definition 1: If $D$ is of the following type: $\bullet \to \bullet$, ...
117 views

### Permutation generation problem using swaps

This is motivated by Aaronson's post, Probability of generating a desired permutation by random swaps. I am interested in a related problem where the swaps are given in the input. We're given as input ...
2k views

### What's the earliest result (outside of logic) that cannot be proven constructively?

Although mathematicians usually do not work in constructive mathematics per se, their results often are constructively valid (even if the original proof isn't). An obvious counter-example is the law ...
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33 views

### complexity of membership problem in finite general linear group

Suppose $G$ is a subgroup of $GL(n,q)$ given by a list of generators. What is known about the complexity of the corresponding "membership problem", that is, the problem of deciding whether a ...
• 2,145
1 vote
21 views

### How to extract 'top k' multiple solutions from a quadratic optimization problem?

Imagine we are interested in the following problem: $$\min_{w} \left( w^T V w + \lambda \|w\| \right) \\ \text{s.t. } w^T R \geq c$$ Where 𝑤 is an $N \times 1$ vector, $V$ is an $N \times N$ ...
• 111
1 vote
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### Upper-bound of the tail of a weighted sum of iid random variables

I have a question related to this one. $X_i$ are n iid random variables with CDF $1_{[0,+\infty[}(x) \Phi(x)$, i.e. it is a mixture between a folded Gaussian and a delta in $0$, both with weight $1/2$....
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### Is the adjoint action of $\mathrm{SU}(2)$ on the Schwartz space proper and free?
$\DeclareMathOperator\SU{SU}$Let $t_1, t_2, t_3$ be generators of the Lie algebra $\mathfrak{su}(2)$. Let us consider a Schwartz space $\mathcal{S}$ defined as \mathcal{S}:= \Bigl\{ \...