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About Countable Dense Homogeneous spaces (CDH) and strongly locally homogeneous spaces

I am new to the study of CDH topological spaces, I wanted to study basic examples of this type of spaces, for example I could understand the demonstration that ...

Asked on 01/03/2022 by Gabriel Medina

Is there an abstract logic that defines the mantle?

It is a known result by Scott and Myhill that the second-order version of $L$ yields $mathrm{HOD}$.Recently, Kennedy, Magidor, and Väänänen (Inner models from...

Lorentzian vs Gaussian Fitting Functions

This is probably too general a question to ask without some specific context, but I'm going to give it a shot anyway: What are the practical differences between using a...

Applications of mathematics in clinical setting

What are some examples of successful mathematical attempts in clinical setting, specifically at the patient-disease-drug level? To clarify, by patient-disease-drug level, I mean the mathematical work is approved to be...

Bounds on number of "non-metric" entries in matrices

Question:what upper bounds are known on the number of non-metric entries of finite dimensional square matrices $boldsymbol{A}inmathbb{R}^{ntimes n}$ with strictly positive off-diagonal elements $a_{ij}$? In this context...

Eigenvalues of convolution matrices

Let $h: mathbb{R}to mathbb{R}$ be a smooth function. Fix $0leq s_1leq cdots leq s_mleq 1$ and $0leq t_1leq cdots leq t_nleq 1$. Construct $Ain mathbb{R}^{mtimes n}$...

Asked on 01/01/2022 by Sina Baghal

Given a large random matrix, how to prove that every large submatrix whose range contains a large ball?

Context. Studing a problem in machine-learning, I'm led to consider the following problem in RMT...Definition. Given positive integers $m$ and $n$ and positive real numbers $c_1$...

Does the $K^1$-group of a complete flag variety vanish?

For $U(n)$ the Lie group of $n times n$ unitary matrices, and $T^n$ its maximal torus subgroup, the homogeneous space$$U(n)/T^n$$is called the...

Asked on 01/01/2022 by Quin Appleby

Does every special $C^*$-Frobenius algebra have a unit?

I have a rather basic question about $C^*$-Frobenius algebras (also called Q-systems). Any pointers or references will be most helpful! We are given a finite-dimensional complex Hilbert space ...

Motives under de-singularization

Let $X$ be a singular variety over a field $k$ of characteristic 0. Suppose a minimal resolution of singularities of $X$, $f:tilde{X} rightarrow X$, exists, i.e.,...