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Mathoverflow.net news digest

  • 0 days

    Derived push-forward of a sheaf in two different categories

    This is a very basic question on sheaf theory.
    Let $f\colon X\to Y$ be a continuous map of topological spaces. Let $\mathcal{O}_Y$ be sheaf of commutative unital rings on $Y$. Let $F$ be sheaf of $f^{-1}(\mathcal{O}_Y)$-modules. Is it true that the derived functors $R^if_*(F)$ in the category of...

  • 5 years

    What kinds of gradient-flows on $\mathbb R^d$ preserve the log-concavity of the ...

    Let $\mu_0$ be a log-concave distribution on $\mathbb R^d$ and let $f:\mathbb R^d \to \mathbb R$ be $C^2$. Let $x_0$ be sampled uniformly at random from a log-concave distribution $\mu_0$, meaning that $\mu_0$ has density of the form $p_0(x) = e^{-U...

  • 12 years

    Can the hyperbolic plane be immersed in three dimensional Euclidean space, if we...

    Consider the following question:
    "Can the hyperbolic plane $(\mathbb{R}^2, g_H)$ be isometricallyimmersed in three dimensional Euclidean space$(\mathbb{R}^3, g_{flat})$?"
    I believe the answer to this question is no. Can someone give me a referencefor this theorem (in particular I want to look at the details of theproof and understand why this is not possible)....

  • 1 month

    Incentivizing mathematics in an era of AI-accelerated proof abundance

    Despite Timothy Gowers's relief that this recent AI solution of the Erdos Unit Distance Problem only involves a counterexample and not a proof in the positive (see the companion document in the link above), it seems appropriate for the community to weigh...

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