geometry-topology / Convex geometry
Ehrhart conjectured that a full-dimensional compact convex body in $\mathbb{R}^n$ whose barycenter is its unique interior lattice point has volume at most $(n+1)^n/n!$. With the inequality itself settled, the remaining question was which bodies attain it. Every such body is a unimodular image of the simplex $(n+1)\Delta_n - (1,\dots,1)$.
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the equality case; the inequality was settled separately and is tracked on its own entry
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Ehrhart conjectured that a full-dimensional compact convex body in $\mathbb{R}^n$ whose barycenter is its unique interior lattice point has volume at most $(n+1)^n/n!$. With the inequality itself settled, the remaining question was which bodies attain it. Every such body is a unimodular image of the simplex $(n+1)\Delta_n - (1,\dots,1)$.
the equality case; the inequality was settled separately and is tracked on its own entry
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