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Mathoverflow.net news digest

  • 0 days

    Iterated free extensions of categories by adjunction residues

    Context & Motivation
    Let $F : \mathcal{A} \to \mathcal{B}$ be a functor between small categories. Under nice conditions (e.g., if $\mathcal{B}$ is cocomplete, or by passing to presheaves), this induces a Kan-extension adjoint triple: $$ \mathrm{Lan}_F \dashv F^* \dashv ...

  • 10 years

    Hausdorff dimension of Apollonian circle packing, 1.305686729, 1.305688 or yet s...

    I am interested in the Hausdorff dimension of the Apollonian circle packing.There seem to be two numerical calculations of the value:
    from P.B Thomas and D.Dhar, The Hausdorf[sic!] dimension of the Apollonian packing of circles Journal of Physics A: Mathematical and General, Volume 27, Number 7, April 1994...

  • 0 days

    Incentivizing Mathematics in a Post-Problem Era

    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...

  • 0 days

    Jordan conjugation with prescribed non-zero leading principal minors

    Let $\mathbb{F}_q$ be a finite field, and assume that $q$ is sufficiently large. Let $X \in \mathrm{M}_n(\mathbb{F}_q)$ be an upper triangular nilpotent matrix whose Jordan form is $J_\mu$, where $\mu$ is a partition of $n$. Is it possible to find a...

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