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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 $c_1$...

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MathOverflow Asked on 2 years ago

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...

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MathOverflow Asked by Quin Appleby on 2 years ago

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 ...

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MathOverflow Asked by quantumOrange on 2 years ago

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.,...

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MathOverflow Asked by user161697 on 2 years ago

Fundamental ring of a circle

Starting with fundamental group, say of a circle, let's reflect back to path groupoid a little. The path concatenation operation is partial, but this can be remedied by focusing on...

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MathOverflow Asked by Tegiri Nenashi on 2 years ago

Reference request: extendability of Lipschitz maps as a synthetic notion of curvature bounds

In the lecture Notions of Scalar Curvature - IAS around 8:00, Gromov states the following result, which he claims he does "slightly uncarefully":Suppose $(X,g_X)$ and ...

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MathOverflow Asked by Lawrence Mouillé on 2 years ago

Should cohomology of $mathbb{C} P^infty$ be a polynomial ring or a power series ring?

Some people define total cohomology of a space $X$ to be $bigoplus_{i geq 0} H^i(X)$, which would make $H^*(mathbb{C} P^infty)$ a polynomial ring in one generator of...

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MathOverflow Asked by PowerToThePeople on 2 years ago

My G Suite Gmail personal emails to people are being sent to spam

I was one of the early adopters of the free G Suite (formerly Google Apps) package from Google. So I set up a little custom domain and email for my...

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Web Applications Asked by bshor on 2 years ago

Change link unfurling image used by Notion

Whenever you post a link to Notion into Slack etc, the image that unfurls is always this: Is...

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Web Applications Asked on 2 years ago

Roman culture for converted CK2 game

I finished Crusader Kings 2 (CK2) where I own the Roman Empire. I converted the save game and bring it to Europa Universalis 4 (EU4). If I were to create...

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Arqade Asked on 2 years ago

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