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Q&A for professional mathematicians
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I hope everyone is doing well. Let $K \subset \mathbb{R}^n$ be a centrally symmetric convex body $(K = -K)$. Denote by $K \mid H$ the orthogonal projection of $K$ onto $H$, where $H$ is an $n - 1$
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Hottest Questions Today - MathOverflow
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Mathoverflow.net news digest
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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...
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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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